Humans know intuitively that causing suffering and death to other animals is morally wrong

You can't prove that it is justifiable to kill animals.
We have the ability to develop intuition, love and compassion for all beings. But it requires that we stop oppressing them. We can intuitively know that it is wrong to cause suffering and to kill another sentient being. However, if we oppress animals routinely as most humans do, we may lose this capacity. Just like persons committing severe moral atrocities may not have comprehended that what they did was morally wrong. I believe that men are goodhearted. However, humans participating in regularly excluding the animals, regularly saying 'I don't care' by the choices made, regularly oppressing them by eating them, wearing them and making other choices that are oppressing the animals, may become very disconnected to the animals, their lives and their inherent moral value.

One can reason like this:
"1. The imposition of suffering on any sentient being requires an adequate moral justification and pleasure, amusement, or convenience cannot suffice as adequate to justify imposing suffering on any sentient being
2. The most “humane” animal agriculture involves considerable suffering imposed on sentient beings
3. As a general matter, our best (and only) justification for eating animal products is pleasure, amusement, or convenience
4. Therefore: We cannot morally justify eating animal products

This is all very logical. But the argument is not going to go anywhere if you don’t accept the first premise and want to act on it. If you do not accept that you have any obligation to justify in a meaningful way the harm you impose on animals, we can’t even get started talking about animal ethics. Logic and rationality can help us to ascertain what we owe nonhuman moral persons but logic and rationality are useless in the face of someone who just does not care morally about animals and who rejects the notion that any justification for the imposition of harm is required.
Science is also useless where the first premise is concerned. There is no way to prove “scientifically” that we have an obligation to justify the imposition of harm on a sentient being. As any first-year philosophy student knows, you cannot derive an “ought” from an “is.

So why should we accept the first premise?
I maintain that the first principle is self-evidently true. All sentient beings matter morally and before I adversely affect the interests of any sentient being, I am obliged to justify my action. When I use “true” here, I mean it in the same sense that I mean it when I say that the cup on my desk is red. The statement, “The cup is red” expresses a true proposition. The cup on my desk is red. Similarly, the statement, “We need to have a morally sufficient justification for imposing suffering on any sentient being” expresses a true proposition that reflects our moral intuition that suffering is bad."
Quote from and continue to read here: http://www.abolitionistapproach.com/moral-concern-moral-impulse-and-logical-argument-in-animal-rights-advocacy/#.USk5sVfA0Wk