I don't think the most effective argument against whaling comes from concerns about their suffering. Same with horse meat.
That would be persuasive to some vegans and vegetarians, but they represent a small subset of the population.
A much larger group will respond well to concerns about their extinction. I want my son, and someday my son's kids (if he has any) and their kids to be able to go whale watching. I don't want them to go to school and learn about extinct species that my generation wantonly destroyed.
Unfortunately, this common desire runs afoul of other cultural activities that a few small minorities want to maintain: they want to follow their parents, and allow their kids to follow them, in hunting and eating whale.
A question for you: the banana tree is at risk of extinction, many historical variants have been pushed out of existence by massive cultivation of sterile farmed varieties. Blight, disease, and other issues put this large population of identical plants at risk.
The difference between the whaling problem and the banana problem is that bananas don't have the ability to experience suffering[citation needed]. Do you think it would be meritorious to advocate for the preservation, cultivation, and careful stewardship of bananas?