Well, actually, although sex is possible (but not mentally or ethically healthy), cross-breeding is not for the same reason humans and farm animals (another popular topic of debate) cannot procreate. Apes have 24 pairs of chromosomes and humans have 23 pairs.
Another reason for the impossibility is that many chromosomes which would be similar are inverted (flipped backwards) between apes and humans (see region p14.I to q14.I in chromosome 5 to see the reversal), and although individual chromosomal inversions do not eliminate the possibility of cross-species fertility, the nine known inversion points between chimpanzees and humans and the twelve inversion points between gorillas and humans makes it nearly impossible
It would be easier, and more likely for an ape to breed with a chimpanzee
And nearly impossible means just that … that yes, if you got a million humans and bred them to a million apes, one or two might result in a crossbreed, but its likely that the crossbreed will suffer the ravages of numerous other chromosomal anomalies that we are not aware of …..
And genetic manipulation could in theory fix all of this, but I have yet to see a reason to do it, but I'm sure someone eventually will try …. I mean, everything else has been tried (as I'm sure some horny person has already tried to mate with an ape somewhere on this planet), so is it possible?
Yes, but so is winning the lottery, would we want it? I don’t think so …. The thought of creating another “Frankenstein” isn’t a very sane one …