It's quite possible that the problem with paradoxes stems not from them being 'impossible', but from our limited cognitive tools failing to equip us to think about them.
Sort of like people in ancient times believing you can't predict the motion of the planets because they didn't have calculus yet.
It's also quite possible that the whole idea of time travel seeming probable stems not from being actually possible, but from human brain cognitive bias of memory. In our head, past events are almost as real as current events, therefore creating obvious illusion of possibility of traveling in reality just like you travel in memories.
Sort of like people in ancient times believing you can't predict the motion of the planets because they didn't have calculus yet.