TL;DR: Domesticated animals deserve death. More specifically, because they letting them live is "inhumane" because they won't thrive without human influence—which they're strictly against.
IMO: These people are fucking psychopaths.
Edit: Yes, that specific site is sponsored by the meat industry. I didn't think it needed to be said, but don't take sensational topics at face value and read any receipts provided (which they did). Or, use Google and find other sources (that are also probably backed by corporate or political interests). In either case, PETA has made it pretty clear that they're hypocrites who are euthanizing healthy animals.