I think a better way to state the premise more reasonably is to say that you don't get to engage in hunting/harvesting practices that risk extinction of the species. That is a position that can be logically consistent with both claims "Farming domesticated animals is okay" and "Whaling is a practice that should be heavily regulated with careful quotas"

You should not eat fish from the sea, then.

At least, we should eat much less fish from the sea. With fishing, as with hunting, the limits need to be what the eco system can sustain. The sad part is, due to our overfishing, the sustainable fishing rates are much lower today than they would have been 100 years ago. If we had not overfished, we could fish much more than we should today. Same applies to whaling in much stronger form.