No a chimp will always be a primate, and a human will always be a primate.
Both just primates? OMG that must mean they can evolve into one another using your logic.
And where did these primates come from?
Did not (according to evolution) they start out as a single cell and then a fish, and they became birds that became primates
That is the vertical evolution we are talking about.
When you find a semi chimp/man let us know.