Why do animals have moral worth?

[DaBankasDaBonuses]

How would being a Catholic imply slavery is wrong but eating meat is fine? Jesus said literally nothing against slavery. The Old Testament at least objected to the mistreatment of slaves, although not to slavery itself, Jesus did not even do that.

Because a Catholic follows his Church's theological interpretation which is that slavery is wrong. This scripture quoting may work on a Protestant but not a Catholic.

No, I did not bring up slavery as a way to trigger your emotions. The point I was making is that it is probably impossible to explain why slavery is wrong without also implying factory farming is.

It's pre-supposed in our society that slavery is wrong. I happen to agree because of my gut feelings and social conditioning but I can't prove it objectively. There are a number of ethical stances (true or not) which claim that humans have particular rights whereas animals do not. Catholicism is one of them.

[teo123]

Because a Catholic follows his Church's theological interpretation which is that slavery is wrong.

In which case, Catholicism is very inconsistent.
As well, any political or ethical theory based on supernatural is very flawed. We do not know if supernatural entities exist. And even if we did know that, claiming we know with reasonable certainty what they want is absurd. And even if we did know what they want, why should we listen to them? They are not of this world, they have no skin in the game, if they even understand what is going on in this world (Why would supernatural entities know what is going on in this world better than we undestand what is going on in their world?). We can know with reasonable certainty there is no afterlife, so those supernatural entities cannot make us suffer in the afterlife if we do not follow their instructions, or reward us if we do.
You really cannot claim deontological or utilitarian or virtue ethics is nearly as wrong as ethics based on supernatural.

It's pre-supposed in our society that slavery is wrong.

How is it pre-supposed? It is based on evidence. Slavery stifled technological progress a lot. It also caused a horrible amount of suffering.

[FredVegrox]

Animals have worth in the sense in which humans, which are animals in the meaningful definition, have worth. It is our own perspective as humans that we find more accorded worth to us humans, which is actually an arbitrary basis.