I know the term speciesism but am not read up enough about it to say whether I would fit that perspective. Personally I don’t believe a human and a bear and a deer are equal, or even two humans are equal, just equal in certain ways that matter when discussing things like the right to their life.

And taking a life can be justified. But I personally would not take a life for food as there are other things to eat. Even if OP believes that neither deer nor bears have the right to life though, I’m curious what line of reasoning would bring someone to think the act of taking one’s life is monstrous and taking another’s noble. Surely to believe such a thing there must at least be some kind of great cost attributed to at the very least killing that bear, and I am curious why that cost would not be also an attribute of killing the deer or be neutralized by the boon of deer meat vs a trophy or the satisfaction of hunting (which the OP claims to be the only reasons someone would hunt a predator, but I can come up with more).

The morality of the situation is certainly an emotional subject for me. But in conversations like these I’m mostly approaching it out of curiosity as I acknowledge that most people find these things normal and am more interested about why they find these things normal or what justifications they come up with on the spot. I believe most people don’t really know why they find these things normal, I’m not sure I really knew why I found them normal before I was myself questioned.