^ This is the correct answer. If you look at the amount of DNA we share with other primates, like, say, the Bonobo, it is clear humans could be re-classified to more accurately reflect our close genetic ties to them.

But, here is the thing: It is we humans who define the categories into which we group genus/species, etc. And we really love to think of ourselves as extra special. So, the idea of including ourselves with a group of non-human animals goes against the grain of society, no matter how genetically accurate it would be.