The animal rights logic is usually the following: Animals have the capacity to suffer and a will to live, therefore they deserve a right to not be harmed or killed needlessly.
No sane person would argue that they should have the right to vote or anything like that, just the basic ones. I feel like there's a lot of confusion about this.
E.g. kicking a dog on a whim violates their right to not be harmed and should be illegal in an ideal world.
It seems like you share the ethical concern. Why wouldn't you be in favor of granting them these two basic rights then?
Maybe your problem is with extending this logic to something like killing a pig for taste pleasure compared to kicking a dog? I'd argue that if you're against the latter, there's no ethical reason to defend or even support the former. Something being culturally ingrained or pleasurable doesn't automatically justify it after all.