It's a very basic conservationist principle. Humans do not, should not, willingly and knowingly contribute to the extinction of species. This rings true for me not only because of the good reasons stated above in terms of the fragility of the Earth's and ocean's ecosystems, but also because whales, along with everything else, are a resource, and the future unborn generations are entitled, in my opinion, to a share of those resources.
The major reason for this would be that whales are a major part of the ocean's ecosystem. If whales were to become extinct, it would disrupt the ocean's ecosystem in ways that are very hard to predict. This might end up causing changes that would have a direct impact on human life or on human economic activity. This would be the most pragmatic argument against whaling -- that making whales extinct could actually harm us as human beings by disrupting an ecosystem that makes up the majority of the surface of the planet.
There are many reasons but the most important thing is that the whole eco-systerm whould change and that effects the human behaviour.
Thank you so much to both :)