Well now, now you’re introducing the next door neighbor’s reasons for what he is doing.
But you want to know why A is upset at you. A is upset at you because A thinks you made a deal with next door neighbor for next door neighbor to not allow A to park in their side of the driveway.
Maybe it was a good deal for neighbor, and maybe you made no deal with neighbor. But that is probably why A is upset at you.
So either tell A that you don’t care if A parks there, or live with A being upset at you.
If you want to know who I think is right, I can give an opinion on that also.