Because we can. The same reason for exploring a new park around the corner or climbing a mountain.
Because it is not optional. For as long as we are here alone, we are on a 100% sure road to extinction. We don't transform, we don't evolve... we disappear. Regardless of when it happens, if it does, tomorrow or two millenia from now, if all our descendants die, it will be as if we never existed: all our lives, our struggles, our achievements will have been meaningless, not even forgotten, but... non existent, eaten up by a entropy like matter that falls into a black hole.
So by simple logical deduction, we either opt in for space exploration, or we might just as well light the fuse now, and save ourselves the trouble. But then we would probably be the most pathetic species in the universe: one that knows what has to be done, has the potential to doing it, even came close to doing it, but opted not to do it.