Agreeing with the position of some other contributors to this thread, and disagreeing with you on this particular point (even though I acknowledge that your position is reasonable, and that your points wrt, say, vegetarianism, etc., despite nismaratwork's eloquent, and to the point, protestations, make much sense to me) I don't think that animal rights, or any other rights are "a given" in any sort of naturalistic, objective sense. Rights are given, or not, by those in power, by those in control.
Now, do I think that Japenese, or Norwegian, or whatever, whaling should be allowed to continue? Personally, I would rather that it stop. But, objectively, wrt the world at large, I can't find a good reason why it should. That is to say, even though it offends my sensibilities, I don't think it matters wrt encompassing considerations such as the survivability of other species, in particular mankind, or the oceans, or Earth. More species than we can count have come and gone in the history of the Earth.
As far as I can ascertain, worst case scenario, all of the whales and dolphins in the world can become extinct, and that wouldn't have much impact on the survivability of the human species. In fact, most of the species in our world can become extinct, and that wouldn't have much impact on the survivability of the human species. Do I want to live in such a world? No. Do I have any reasons for this orientation other than emotional ones? No.
I don't think in terms of normative ethics. Esthetically, for reasons that I can't verbalize, I would rather that we leave populations of wild animals to flourish, or not, on their own. However, it appears that certain portions of humankind are intent on preying on, with the possibly of extinguishing, certain animal species. And, I don't have any good, objective, argument against this, while very much not liking it.
Are the Japanese or Norwegian whaling practices reprehensible? Well, not according to them. And I have to agree, in a certain sense. Whale killing, or rhino killing, or gorilla killing, or whatever, isn't, in itself, reprehensible. Ok, yes, I, along with many others, want to live in a world where all of these species are present. However, my current opinion is that it doesn't matter wrt to the survivability of humankind. So, if the criterion is simply the survivabilty of humankind, then it seems to me that we can kill off most of the animal and plant species on Earth and still survive quite healthily. Or maybe not. I don't really know, so am amenable to being persuaded otherwise.