It is arbitrary, and it is not at all about the right of the stronger. For example, implicit in that axiom is that a weaker human is considered more "valuable" than a strong animal.
You have to take an arbitrary position to start with. There are only three possibilities:
1) humans are more important than any other animals
2) humans are as important as some animals
3) humans are just as important as any other animal
Take your pick and explain why the first is less moral. I think you are confusing morals with a (misguided) attempt at coherence ("respect every living creature" hippie stuff). Personally I could make up "moral" arguments against any of those.
But I must point out that the third is also suicidal if one were to interpret it as "we must respect all other animals" as, inevitably, we're going to kill more than a few over the course of out natural lives. And the only other possible interpretation for 3) would be "we should use and kill other humans just as we use and kill animals".
I may as well go into detail and explain (again) why I disapprove of 2). And I have two reasons to disapprove. One is logic: because the choice of those some animals to protect will be made by humans, which will have to assume the role of judges - thus the very act of proclaiming some animals "equal to humans" affirms the superiority of the humans doing it... logical contradiction! And the other is moral: people are bound to disagree on which animals to protect, setting humans against humans allegedly for the sake of protecting animals, in reality for the sake of enforcing some human's preferences over those of others. Hardly a paragon of morality, to oppress fellow humans for the sake of some baby seals on the Arctic or "sea kittens" or whatever.
Really, there is no moral high ground on this, actually, it's a matter of preferences. And that's what irks me the most whenever those animal rights activists try to force laws to impose their worldview, and do it with all smug with presumed moral superiority.