Correction, humans are a species of ape. And the whole fish stay fish thing is somewhat accurate. Organisms can only evolve from what they are. So that's close. But think of a family tree. In a family tree, a couple has some kids, and then those kids have kids, and so on, until the tree is very large and somewhat complex. If you keep tracking the tree long enough, eventually you'll have a generation where those at one side wouldn't traditionally be considered related to those at the other side. Keep going, and let's say one side of the tree, or population, gets geographically isolated from the other side. That same tree keeps going, but now in two very different directions. After many many years, of the two different populations experiencing different natural selection pressures because of their different environments, they will eventually become different species. So when you consider the family tree as each branch an entire species, instead of individuals, you can see how evolution works. So yes fish will only have descendants of fish, but what they look like after enough time can be so different that you'd never know they were related by just looking. All those unique individuals passing on their changes to make more unique individuals across millions of years and generations results in what we see today.