And animals and humans cannot mate and produce offspring together
And you know this how, exactly? Human sperm have been shown to be able to penetrate the ovum of a gibbon - a primate, but far removed from humans/chimps. Now "penetrate" isn't "fertilize," but I'm not sure you can catagorically say that humans and chimps aren't interfertile. And no, I'm not advocating experiments to test it out - not beyond the second cell division, anyway.
Lions and tigers are interfertile to at least some degree, and I'll bet a shiny nickel that those two differ more genetically than man and chimp.