Question: so what if whales go extinct and we lose a bit of biodiversity?
Very valid question. I suppose it's a matter of cultural and monetary loss, environmental impact, and partially of subjective value judgment.
If a species goes extinct because it was over-hunted, it can be assumed that those hunting it placed value on its continued existence. Any cultures placing value on it for food, material goods production, religion, etc. lose that just as much as if it had been banned. The difference is that they cannot ever get it back. I do believe this constitutes a notable loss to humanity. When the population is allowed to re-expand, however, eventually there can be more whaling (still limited, of course) and perhaps there could eventually be an open market.
Secondly, most species fill a particular niche in their ecosystem and to have that niche become empty can pose very serious problems. Sometimes other species compensate and the ecosystem balances back out, but sometimes it does not and the extinction of a single type of animal can lead to that of numerous others. This usually spreads from animals to plant life, which can cause serious geographic repercussions.
Finally, some people (myself included) place value on the existence of an animal in and of itself. The loss of biodiversity can be mourned whether or not it changes the world for humans... if that is what you believe. As a Christian, I think we are called to be good stewards of the Earth; to use it within the bounds of sustainability. It is a beautiful creation and to knowingly destroy parts of it is as disgusting as destroying a precious work of art. Again, it's a very subjective reason.