See I don't believe that it is 'morals' that separate us. We ARE animals, with no more inherent or objective virtue than any pig or chimp.
The only thing that makes us different is our huge brains, which have enabled us to effectively take over the planet (and ironically also to wreck it), whilst still having brainspace left over to invent/ornament a whole bunch of inessential made-up stuff stuff like games, literature, music, art, religion and morality.
Morality, because it is made up, is relative. The only 'morals' that hold fast across pretty much all human cultures are ones that have a pretty strong basis in evolutionary necessity and other mammals by and large share them.
Otherwise our 'moralities' vary enormously and evolve/attenuate over time based on exigent circumstances. Once upon a time homosexuality was 'immoral' (and still is in a number of cultures). Incest is 'immoral' to varying degrees in differing cultures (so in the UK we'd be pretty repulsed by marriage between first cousins nowadays, whereas it is quite normal in other cultures. Multiple wives is considered immoral in our culture but perfectly acceptable in others. Suicide and even murder/suicide has at various times in various cultures (and even within the same culture) been considered evil, honourable, required or morally neutral depending on its social effect.
So to my mind the idea there is some sort of 'true' morality that all/most human beings inherently share that animals do not is not demonstrable or a good argument for legislation. I would love it if things were different, and that 'my' morality was entirely 'correct' and objective, but it absolutely isn't. Any more than yours is, or a lioness's is, or a kamikaze pilot's is.