It isn't "survival of the fittest," or at least it shouldn't be; it's "survival of the fitted." As long as environments exist to which modern apes are fitted, they will survive.
That's a good answer, but why was our ape-line more fitted to evolve into humans than the apes living under the same conditions? I'd buy into a random mutation better than evolution of the fitted, because that means physical changes due to better adaptation to the environment. Instead we have a different set of genes.
There's a lot to be said for evolution but most arguments for it can't quite make me get over the hump of scepticism.
Actually, I think the universe was started by my Uncle Roy, the clockmaker, in a previous billion year-old incarnaion. Beyond that I'm not prepared to go.