Humans are enjoined to make each other happy, including by cooperating in accordance with the deliverances of economics; religion enlivened by the grace of God goes further and teaches that they ought to have charity for each other.
Now murder is a black sacrament of either (1) hatred or (2) madness, which is why it is forbidden.
Certainly, hatred for fellow man is a ticket to hell.
Assuredly, we also ought not to hate animals or take pleasure in their suffering. Even mosquitoes, though enemies of mankind to be exterminated en masse, should not be hated but killed dispassionately. But when cows are slaughtered, it’s pretty clear the farmers are not being sadists, so condition (~1), absence of hatred, is fulfilled.
But a man who kills another man even without any hatred in his heart (such as when Elmer murders his grandfather for the inheritance) still is a monster for failing to recognize a creature who benefits rather than harms him while alive for what it is. All humans are useful to each other according to natural law (and their mutual usefulness happens to be maximized under laissez-faire). To fail to grasp a fact so basic is to be insane.
(I am saying of course that the proposition “murder is wrong” can be rigorously proven by reducing something like a Crusoe-Friday relationship to pure self-interest. I do not mean that in daily life people decide whom to kill and whom to spare by calculating which of their fellows are useful to them at any given moment and which are not.)
But a cow is not useful to a man in the same manner that a fellow man is useful to him. Hence, the reasons why it is (even naturally without grace) rational to abstain from murder do not apply to killing a cow for its meat. Condition (~2), sanity, is also present.
Nor does it seem that more pain and suffering are created when animals are slain by humans, such as instantly by an electric shock, than when they are killed by predators or die from disease or by being slowly eaten alive in old age.
Consequently, it seems permissible by natural morality to kill animals for food, etc.
See also: Animal Are Fully at Our Mercy.