It's really not, they're not the same thing at all. You even use the phrase "slippery slope" which is a type of logical fallacy. What you're saying is, "you're sexually attracted to animals, so clearly you're going to want to torture them." The sillyness of the argument is obvious if you simply change the group, "you're sexually attracted to people of the opposite sex, so clearly you're going to want to torture them."

I think beliefs like this typically stem from 1 of 2 places: their own desire to torture and inflict pain or, more commonly, a misrepresentation of zoophilia with the more visible zoosadism. It makes sense that most exposure to non-human attraction comes from the horrors of zoosadism, but that doesn't mean all zoophiles are that kind of monster. If that's what guides your opinion, I suggest you to learn more about us and see that so many of us have no desire to hurt animals in any way. If your opinion comes from your own sadistic desires, I urge you to seek professional help to manage those thoughts.