Suppose it were somehow possible to prove that alien life exists. Like, we get a radio signal saying "hey, Earth! We see you looking at us!" that's conclusive and undeniable.
That would upend a lot of religious teachings which say we're unique and that the world was given to us, as the unique creations of a creator, to consume for our own benefit.
It seems like there could be many practical benefits to showing that's not true. Hey, maybe the concept of infinite exponential growth is a bad idea. Maybe we shouldn't burn the skies and boil the seas. Maybe we should be nice to other intelligent animals, at the very least.