[@Tip]

It's a sort of nod/easter egg to the HPMOR fanfic.

There, there is a plot point about animal patronuses being incomplete forms of the True Patronus. Animal patronuses are maintained with happy thoughts, which basically defeat the dementors, Death anthropomorphized, by making their casters fearless in the face of death (animals are not aware of death in the abstract, which is why dementors don't drain them). The True Patronus, on the other hand, is maintained with ambition, the will to actually fight Death itself and reach immortality rather than simply not fearing it, and is represented by a humanoid rather than an animal.

David's mindset is closer to the second than the first, but not quite there, so he gets a chimpanzee, the animal most similar to a human.