Why do airliners park with the nose facing the terminal?
To park a passenger plane with its tail towards the terminal has several disadvantages:


it would require a pushback tractor (plus personnel) to do that. Thrust reversers in general are not meant for making the plane go backwards. If it was possible for the plane to go autonomously backwards, it would be extremely = too risky.
you would also need the pushback tracktor for leaving the gate, you couldn't use engines because of the jetblast hitting the terminal
you could not use the APU because it would scorch the terminal
the horizontal tail of some planes might have clearance issues with the jet bridge.
last but maybe not least: the upper class travelers. They sit at the front for a reason: they get on and off the plane first. Yes, the business and first class could be moved to the back. Now, I don't know if riding closer to the cockpit rather than the arse of the plane has some intrinsic value, but at least it is usually noisier at the back.
So customer satisfaction might take a hit there.


So: twice the hassle with pushback + other issues, with no benefits whatsoever.