If Man Evolved From Ape, Then Why Are There Still Apes?

Firstly, man did not evolve from modern apes. Man and modern apes share a common ancestor, which is extinct. However, the question comes from a flawed understanding of how evolution works. Evolution is not a straight line, where entire populations change into new species all at the same time. Often times, a small group breaks away from a population and begins to evolve independently of the source group. The source group does not need to go extinct, and is generally unaffected by the development of the smaller group.  This is called "Allopatric Speciation," and it is just one of many ways that new species can evolve. There is nothing in evolutionary theory which states a source population must go extinct in order for new species to evolve.