Each generation is a tiny bit different compared to the previous. Split a population of animals into two based on a geographical divider or so, make the circumstances slightly different so that slightly different traits give better survivability in each group, and over a long long time they'll drift apart. Then humans come along and decide they're different enough to call them different species.
But if the original species was an ape, then both new groups are still apes. Just like they stay mammals, just like they stay arthropods.
We can do genetic analysis that shows the above to have happened all the time, and by looking at which genes two species have in common and which have diverged we can estimate how long ago the last common ancestors lived.
And the last common ancestor of humans and chimpanzees is more recent than the last common ancestor of humans and orang utans (that ancestor is also the last common ancestor of chimpanzees and orang utans, of course).
So if chimpanzees and orang utans are apes, then we must also be apes.