It is slightly absurd to talk of animal rights when there is no given reality of the human animals rights, it has confered certain rights on other members of it's species through organization. Admittance to this process from the animal kingdom would imply they had a standing in our communal set besides the standard issue;
We
do currently treat all other members of large classes/orders as food or resource, tradeable. We might alter our propensity by altering our value structures in the future but it would need very subtle reevaluations.
In the case of the Whale, it is too late, we probably are going to consign them (our largest mammal relative) to the ghost DNA pile;
It isn't a matter of us suddenly putting our foot on the animals head. Their fate was sealed when the first motorized propeller screw put it's industrial rhythm in the oceans; we nuked their internet; whalesong, which is complex, appended and had covered the extent of Earth's Oceanspace for millions of years as a true long-distance communication. They've been pretty much phuked and in a goth downer ever since. The more Giant White Steaks (ime thinkin' shallott&whtwine garnish) we get on our plates the faster we put this animal out of it's post-net misery, folks