The answer is simple -- the fact that one species branches off from another species doesn't mean the initial species must die off. There are any number of counterexamples.

Also, the simian species from which we evolved in fact no longer exists. I emphasize this is just a coincidence and doesn't prove one or another point about evolution.

Darwin's finch species from the Galapagos Islands all coexisted, even though most of them branched off from each other, or from a single initial species. There is no reason to assume a priori that species B, which branches from species A, requires that species A must go extinct.

Humans and monkeys came from a common ancestor. The evolved independently from that point.

Because we didn't come from monkeys, we both came from a common ancestor that is no longer around.