This is really long but I wanted to put as much info as possible:

University has been very busy for me, but I try to make time for my friends when the schedule fits. Sometimes I have to postpone a hangout to a later hour or reschedule for a different date, but majority of my friends understand as we have work, school, studying, etc. I've also been helping my best friend move out of my house into his own place as soon as possible. 

One of my friends I've known since freshman year of high school asked to hang out on a Saturday. I said sure, and I was excited because I haven't seen her in a while. I can say that we're quite close, because I would walk past her house, text her if she's home, and if she was she'd open the door a minute later and invite me inside. Anyway, on the Saturday we were supposed to hang out, she says she can't. That's fine with me, I needed to study that night. 

The next morning I'm at work and my best friend tells me that his house was ready for him to finally move into and so around lunch time, I message her if we can move it to a later hour. The response I got wasn't what I expected. She was upset and said "nevermind, i'm going to do some homework." I realized that she was upset, and so I thought I'll give her some space and not text back.

The next day she messages me and says "you really hurt my feelings after not hanging out with me yesterday." I told her that I did text her if we can move it to a later hour of the day and that I would have hung out with her all night. This led to her saying that she really wanted to hang out and she said she "guessed that i didn't feel the same way." I was shocked and I told her to not jump to conclusions because that's not how I felt. She then emphasizes the time we were supposed to hang out, and said I pushed our plans out of the way, and then out of nowhere asks me if i don't like being friends with her anymore. I told her that's not why, and that i already told her my reason of pushing it to a later hour and that there was no hidden or underlying meaning in my words.

She asks me "Why do i feel sad then?" I tell her I don't know why and only she knows. She then tells me she feels like I'm unreliable and that I was more reliable. ??? I asked her in what ways can i improve and why was it upsetting that I postponed our hangout even though moving his things would only take 2 hours. She said she felt so alone and that no one wants to talk to her. I said that's not true, you have your online friends that you've even visited out of state and you skype with them every week. I also said that if she wanted to start making friends, why doesn't she try joining clubs at our university like I did because that's how I made more friends. She responded with how she doesn't want to make acquaintances, she wants friends (but acquaintances are a possible start to a friendship???) and that a friend is someone to count on and she was disappointed in me. 

I told her I was upset and I didn't want to say anything irrational and wanted to step out of the conversation. She just replied with ok. It's been a week and she finally messages me and says she's still upset but wants me to apologize because i'm "not just a friend, but family."

I feel like there is nothing to apologize for. I communicated with her clearly with why I was postponing our hangout. I find it hypocritical she was upset at me when we didn't even hang out on the original day we were supposed to. 
