Why intergalactic travel is impossible?
It is not impossible! It is just impractical.
Given what we know about physics and space, it IS possible to travel from one galaxy to another. The impractical side is that anyone or living thing is not likely to be the same (or alive) at the arrival.
It takes a great amount of time to travel a great amount of distance - even relativistically. BUT, that doesn't make it impossible - just inconvenient to some intents.