While H is an unlikely criterion for direct ethical consideration (it could justify genocide in specific circumstances!), it is an important indirect factor. Most humans have much more empathy for fellow humans than for nonhuman animals. While this is not a criterion for giving humans more ethical consideration per se, it is nevertheless a factor that strongly influences ethical decision-making in real-life.

This objection doesn't work if you rigidify over the beings you feel sympathy toward in the actual world, given your present mental capacities. And that is clearly the best version of this view, and the one that people probably really mean when they say this. On this version of the view, you don't say that if you didn't care about humans, human's wouldn't matter. You do have to say, "If it actually turns out that I don't care about humans, then humans don't matter." Of course, you might want to change the view if things (very unexpectedly!) don't turn out that way.

I don't think this version gives animals no weight, but I think it typically gives animals less weight than humans. (Disclaimer that should be unnecessary: I recognize that there are other objections to H. It is not necessary to respond to what I have said by raising a distinct objection to H.)