Let's say I've thought about it for 5 minutes and still disagree. Can you walk me through what you think I'm missing?

I'm stuck on what the concept of a "slave animal" even means.

For the purposes of this discussion, it means treating an animal in such a way that if you treated a human that way, it would be slavery. Such as a horse in a fenced pasture that is sometimes ridden.

Are children slaves?

There are a lot of definitions, but generally when talking about slavery in the West people are talking about chattel slavery, which children are not, because they cannot be bought and sold at will.