if one cares about suffering, one should also care about nonhuman animals

This assumes that if I care about suffering, my utility function places some negative weight on suffering much in the same way it places a positive weight on me eating food I like, but this need not be the case. If I care about suffering, it means I want less of it, but it doesn't mean that I'm willing to give up much to reduce the amount. Ceteris paribus, I want less suffering in the world, but that doesn't mean I care enough about it to not eat delicious hamburgers, or even to pay more for a burger. I care about not getting dust specks in my eye too, but if I got one dust speck in my eye per month, and I could get rid of it by never eating burgers, I'd keep eating burgers. It doesn't mean that I don't care, though.