Q:

Can't login to a remote machine with key

I used to login to a remote machine( I have to root of this machine) using key. Both my local machine and remote machine is in f23. From last few days, I can't login to this machine using key. It is asking for password. Here is the ssh -vvv:
ssh -vvv aveta
OpenSSH_7.1p1, OpenSSL 1.0.2d-fips 9 Jul 2015
debug1: Reading configuration data /home/rudra/.ssh/config
debug1: /home/rudra/.ssh/config line 4: Applying options for aveta
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 56: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to phy-aveta.physics.uu.se [130.238.194.143] port 22.
debug1: Connection established.
debug1: identity file /home/rudra/.ssh/id_rsa type 1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_rsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_dsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_dsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ecdsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ecdsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ed25519 type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_7.1
debug1: Remote protocol version 2.0, remote software version OpenSSH_7.1
debug1: match: OpenSSH_7.1 pat OpenSSH* compat 0x04000000
debug2: fd 3 setting O_NONBLOCK
debug1: Authenticating to phy-aveta.physics.uu.se:22 as 'rudra'
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:16
debug3: load_hostkeys: loaded 1 keys from phy-aveta.physics.uu.se
debug3: order_hostkeyalgs: prefer hostkeyalgs: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1
debug2: kex_parse_kexinit: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-ed25519-cert-v01@openssh.com,ssh-rsa-cert-v01@openssh.com,ssh-ed25519,ssh-rsa
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group14-sha1
debug2: kex_parse_kexinit: ssh-rsa,ecdsa-sha2-nistp256,ssh-ed25519
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug1: kex: server->client chacha20-poly1305@openssh.com <implicit> none
debug1: kex: client->server chacha20-poly1305@openssh.com <implicit> none
debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64
debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ecdsa-sha2-nistp256 SHA256:F34tt6QLRDt6Qm45eHOFhYGS5DSxYrThhR2lbBHNXes
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:16
debug3: load_hostkeys: loaded 1 keys from phy-aveta.physics.uu.se
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:14
debug3: load_hostkeys: loaded 1 keys from 130.238.194.143
debug1: Host 'phy-aveta.physics.uu.se' is known and matches the ECDSA host key.
debug1: Found key in /home/rudra/.ssh/known_hosts:16
debug2: set_newkeys: mode 1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug2: set_newkeys: mode 0
debug1: SSH2_MSG_NEWKEYS received
debug1: Roaming not allowed by server
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug2: key: /home/rudra/.ssh/id_rsa (0x562e17c87070),
debug2: key: /home/rudra/.ssh/id_dsa ((nil)),
debug2: key: /home/rudra/.ssh/id_ecdsa ((nil)),
debug2: key: /home/rudra/.ssh/id_ed25519 ((nil)),
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug3: start over, passed a different list publickey,gssapi-keyex,gssapi-with-mic,password
debug3: preferred gssapi-keyex,gssapi-with-mic,publickey,keyboard-interactive,password
debug3: authmethod_lookup gssapi-keyex
debug3: remaining preferred: gssapi-with-mic,publickey,keyboard-interactive,password
debug3: authmethod_is_enabled gssapi-keyex
debug1: Next authentication method: gssapi-keyex
debug1: No valid Key exchange context
debug2: we did not send a packet, disable method
debug3: authmethod_lookup gssapi-with-mic
debug3: remaining preferred: publickey,keyboard-interactive,password
debug3: authmethod_is_enabled gssapi-with-mic
debug1: Next authentication method: gssapi-with-mic
debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug1: Unspecified GSS failure.  Minor code may provide more information

debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug2: we did not send a packet, disable method
debug3: authmethod_lookup publickey
debug3: remaining preferred: keyboard-interactive,password
debug3: authmethod_is_enabled publickey
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/rudra/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Trying private key: /home/rudra/.ssh/id_dsa
debug3: no such identity: /home/rudra/.ssh/id_dsa: No such file or directory
debug1: Trying private key: /home/rudra/.ssh/id_ecdsa
debug3: no such identity: /home/rudra/.ssh/id_ecdsa: No such file or directory
debug1: Trying private key: /home/rudra/.ssh/id_ed25519
debug3: no such identity: /home/rudra/.ssh/id_ed25519: No such file or directory
debug2: we did not send a packet, disable method
debug3: authmethod_lookup password
debug3: remaining preferred: ,password
debug3: authmethod_is_enabled password
debug1: Next authentication method: password
rudra@phy-aveta.physics.uu.se's password: 

I have  deleted .ssh, .config and .cache from the remote and redo ssh-copy-id, without any help.
To troubleshoot, I have createed another user, did ssh-copy-id and that one is working fine. ssh -vvv for that working machine is:
ssh -vvv rudra2@phy-aveta.physics.uu.se 
OpenSSH_7.1p1, OpenSSL 1.0.2d-fips 9 Jul 2015
debug1: Reading configuration data /home/rudra/.ssh/config
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 56: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to phy-aveta.physics.uu.se [130.238.194.143] port 22.
debug1: Connection established.
debug1: identity file /home/rudra/.ssh/id_rsa type 1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_rsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_dsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_dsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ecdsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ecdsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ed25519 type -1
debug1: key_load_public: No such file or directory
debug1: identity file /home/rudra/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_7.1
debug1: Remote protocol version 2.0, remote software version OpenSSH_7.1
debug1: match: OpenSSH_7.1 pat OpenSSH* compat 0x04000000
debug2: fd 3 setting O_NONBLOCK
debug1: Authenticating to phy-aveta.physics.uu.se:22 as 'rudra2'
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:16
debug3: load_hostkeys: loaded 1 keys from phy-aveta.physics.uu.se
debug3: order_hostkeyalgs: prefer hostkeyalgs: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1
debug2: kex_parse_kexinit: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-ed25519-cert-v01@openssh.com,ssh-rsa-cert-v01@openssh.com,ssh-ed25519,ssh-rsa
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group14-sha1
debug2: kex_parse_kexinit: ssh-rsa,ecdsa-sha2-nistp256,ssh-ed25519
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: 
debug2: kex_parse_kexinit: first_kex_follows 0 
debug2: kex_parse_kexinit: reserved 0 
debug1: kex: server->client chacha20-poly1305@openssh.com <implicit> none
debug1: kex: client->server chacha20-poly1305@openssh.com <implicit> none
debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64
debug1: kex: curve25519-sha256@libssh.org need=64 dh_need=64
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ecdsa-sha2-nistp256 SHA256:F34tt6QLRDt6Qm45eHOFhYGS5DSxYrThhR2lbBHNXes
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:16
debug3: load_hostkeys: loaded 1 keys from phy-aveta.physics.uu.se
debug3: hostkeys_foreach: reading file "/home/rudra/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /home/rudra/.ssh/known_hosts:14
debug3: load_hostkeys: loaded 1 keys from 130.238.194.143
debug1: Host 'phy-aveta.physics.uu.se' is known and matches the ECDSA host key.
debug1: Found key in /home/rudra/.ssh/known_hosts:16
debug2: set_newkeys: mode 1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug2: set_newkeys: mode 0
debug1: SSH2_MSG_NEWKEYS received
debug1: Roaming not allowed by server
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug2: key: /home/rudra/.ssh/id_rsa (0x55c98f7eb080),
debug2: key: /home/rudra/.ssh/id_dsa ((nil)),
debug2: key: /home/rudra/.ssh/id_ecdsa ((nil)),
debug2: key: /home/rudra/.ssh/id_ed25519 ((nil)),
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug3: start over, passed a different list publickey,gssapi-keyex,gssapi-with-mic,password
debug3: preferred gssapi-keyex,gssapi-with-mic,publickey,keyboard-interactive,password
debug3: authmethod_lookup gssapi-keyex
debug3: remaining preferred: gssapi-with-mic,publickey,keyboard-interactive,password
debug3: authmethod_is_enabled gssapi-keyex
debug1: Next authentication method: gssapi-keyex
debug1: No valid Key exchange context
debug2: we did not send a packet, disable method
debug3: authmethod_lookup gssapi-with-mic
debug3: remaining preferred: publickey,keyboard-interactive,password
debug3: authmethod_is_enabled gssapi-with-mic
debug1: Next authentication method: gssapi-with-mic
debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug1: Unspecified GSS failure.  Minor code may provide more information

debug1: Unspecified GSS failure.  Minor code may provide more information
No Kerberos credentials available

debug2: we did not send a packet, disable method
debug3: authmethod_lookup publickey
debug3: remaining preferred: keyboard-interactive,password
debug3: authmethod_is_enabled publickey
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/rudra/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Server accepts key: pkalg ssh-rsa blen 279
debug2: input_userauth_pk_ok: fp SHA256:xT3VPQUunB3Nv/Pmi6C6Sroc0fa9SlKcQ4d0eF2vxzI
debug3: sign_and_send_pubkey: RSA SHA256:xT3VPQUunB3Nv/Pmi6C6Sroc0fa9SlKcQ4d0eF2vxzI
debug1: Authentication succeeded (publickey).
Authenticated to phy-aveta.physics.uu.se ([130.238.194.143]:22).
debug1: channel 0: new [client-session]
debug3: ssh_session2_open: channel_new: 0
debug2: channel 0: send open
debug1: Requesting no-more-sessions@openssh.com
debug1: Entering interactive session.
debug1: client_input_global_request: rtype hostkeys-00@openssh.com want_reply 0
debug2: callback start
debug2: fd 3 setting TCP_NODELAY
debug3: ssh_packet_set_tos: set IP_TOS 0x10
debug2: client_session2_setup: id 0
debug2: channel 0: request pty-req confirm 1
debug1: Sending environment.
debug3: Ignored env XDG_VTNR
debug3: Ignored env XDG_SESSION_ID
debug3: Ignored env HOSTNAME
debug3: Ignored env SHELL
debug3: Ignored env TERM
debug3: Ignored env XDG_MENU_PREFIX
debug3: Ignored env VTE_VERSION
debug3: Ignored env HISTSIZE
debug3: Ignored env XCRYSDEN_SCRATCH
debug3: Ignored env WINDOWID
debug3: Ignored env QTDIR
debug3: Ignored env QTINC
debug3: Ignored env QT_GRAPHICSSYSTEM_CHECKED
debug3: Ignored env XCRYSDEN_TOPDIR
debug3: Ignored env USER
debug3: Ignored env LS_COLORS
debug3: Ignored env DESKTOP_AUTOSTART_ID
debug3: Ignored env SSH_AUTH_SOCK
debug3: Ignored env SESSION_MANAGER
debug3: Ignored env PATH
debug3: Ignored env MAIL
debug3: Ignored env DESKTOP_SESSION
debug3: Ignored env QT_IM_MODULE
debug3: Ignored env XDG_SESSION_TYPE
debug3: Ignored env PWD
debug1: Sending env XMODIFIERS = @im=ibus
debug2: channel 0: request env confirm 0
debug1: Sending env LANG = en_GB.UTF-8
debug2: channel 0: request env confirm 0
debug3: Ignored env MODULEPATH
debug3: Ignored env GDM_LANG
debug3: Ignored env LOADEDMODULES
debug3: Ignored env GDMSESSION
debug3: Ignored env SSH_ASKPASS
debug3: Ignored env HISTCONTROL
debug3: Ignored env HOME
debug3: Ignored env XDG_SEAT
debug3: Ignored env SHLVL
debug3: Ignored env GNOME_DESKTOP_SESSION_ID
debug3: Ignored env XBANDPATH
debug3: Ignored env XDG_SESSION_DESKTOP
debug3: Ignored env LOGNAME
debug3: Ignored env QTLIB
debug3: Ignored env DBUS_SESSION_BUS_ADDRESS
debug3: Ignored env MODULESHOME
debug3: Ignored env LESSOPEN
debug3: Ignored env WINDOWPATH
debug3: Ignored env XDG_RUNTIME_DIR
debug3: Ignored env DISPLAY
debug3: Ignored env XDG_CURRENT_DESKTOP
debug3: Ignored env XAUTHORITY
debug3: Ignored env BASH_FUNC_module()
debug3: Ignored env BASH_FUNC_scl()
debug3: Ignored env _
debug2: channel 0: request shell confirm 1
debug2: callback done
debug2: channel 0: open confirm rwindow 0 rmax 32768
debug2: channel_input_status_confirm: type 99 id 0
debug2: PTY allocation request accepted on channel 0
debug2: channel 0: rcvd adjust 2097152
debug2: channel_input_status_confirm: type 99 id 0
debug2: shell request accepted on channel 0
Last login: Mon Oct 12 12:33:15 2015 from 130.238.194.90
[rudra2@phy-aveta ~]$ debug2: client_check_window_change: changed
debug2: channel 0: request window-change confirm 0

I am clueless why in same local-remote combination, one is working and other is not. 
EDIT .ssh/config for the failed one is:
Host aveta
  User rudra
  Hostname phy-aveta.physics.uu.se
  ForwardX11 yes

There is no ssh/.config entry for rudra2, i.e. that worked.
Ans to Paul
in my local machine I have:
tree .ssh/
.ssh/
├── authorized_keys
├── config
├── environment
├── id_rsa
├── id_rsa.pub
└── known_hosts

In both the remote user, I only have authorized_keys. And both are identical.
[root@phy-aveta rudra2]# diff .ssh/authorized_keys /home/rudra/.ssh/authorized_keys 
[root@phy-aveta rudra2]# 

Edit 2: Without using ssh/.configI have commented out the part for first user in .ssh/config. 
 http://ur1.ca/nzndx is the ssh -vvv for that. It is still asking for password
Edit: Permission
The first user...failed one
#ls -al /home/rudra/|grep .ssh
drwx------.  2 rudra rudra  4096 Oct 12 14:16 .ssh
$ls -alF .ssh/
total 12K
drwx------.  2 rudra rudra 4.0K Oct 12 14:16 ./
drwxrwxr-x. 36 rudra rudra 4.0K Oct 12 14:30 ../
-rw-------.  1 rudra rudra  394 Oct 10 12:01 authorized_keys

For 2nd user
# ls -al /home/rudra2/|grep .ssh
drwx------. 2 rudra2 rudra2 4096 Oct 12 14:16 .ssh
$ ls -alF .ssh/
total 12
drwx------. 2 rudra2 rudra2 4096 Oct 12 14:16 ./
drwx------. 4 rudra2 rudra2 4096 Oct 12 14:14 ../
-rw-------. 1 rudra2 rudra2  394 Oct 11 09:57 authorized_keys

A:

There it is.  Group has write access to ~rudra:
$ls -alF .ssh/ total 12K
drwx------.  2 rudra rudra 4.0K Oct 12 14:16 ./
drwxrwxr-x. 36 rudra rudra 4.0K Oct 12 14:30 ../
-rw-------.  1 rudra rudra  394 Oct 10 12:01 authorized_keys

Thus, sshd refuses to trust the files in ~rudra, and does not use ~rudra/.ssh/authorized_keys, even though its permissions are correct.
chmod g-w ~rudra ought to fix it.

A:

Your first user submits the rsa key and it's rejected.
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/rudra/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password

Your second user succeeds
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /home/rudra/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Server accepts key: pkalg ssh-rsa blen 279
debug2: input_userauth_pk_ok: fp SHA256:xT3VPQUunB3Nv/Pmi6C6Sroc0fa9SlKcQ4d0eF2vxzI
debug3: sign_and_send_pubkey: RSA SHA256:xT3VPQUunB3Nv/Pmi6C6Sroc0fa9SlKcQ4d0eF2vxzI
debug1: Authentication succeeded (publickey).

Your command lines are different and your local .ssh/config is being activated for the first user for remote host aveta:
debug1: Reading configuration data /home/rudra/.ssh/config
debug1: /home/rudra/.ssh/config line 4: Applying options for aveta
debug1: Reading configuration data /etc/ssh/ssh_config

What options are you using in the config file ?
Lastly the two rsakeys used appear to be different.
First user
debug2: key: /home/rudra/.ssh/id_rsa (0x562e17c87070),

Second user
debug2: key: /home/rudra/.ssh/id_rsa (0x55c98f7eb080),

