B757-200
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Conflict Ground Conflict; Critical; Ground Event / Encounter Other / Unknown
Human Factors
During pushback; Ramp directed we push back far enough so a heavy jet could enter the ramp and proceed to the gate. As we were pushing back; not yet in place; both my FO (First Officer); and I noticed the heavy jet begin taxiing. My FO commented; what is he doing; and when I looked up it appeared the right wing of the heavy jet was going to hit our flight deck windows. Luckily this did not occur but it was too close for our comfort. What is the hurry - do we not all get paid by the minute. This is simply not acceptable. I called Ramp to ask whether or not this was a revenue flight and was told this was Aircraft Y arriving from ZZZ1.The inbound all night flight's Captain decided to taxi before we were fully clear of their wing. Do not be in such a hurry to taxi and ensure you are fully clear of another aircraft before beginning your taxi. The company has had too many ground collision events over the last two years - and I guess the message has not gotten out to all the crews.
B757 Captain reported encountering a near miss with another taxiing aircraft.