> Even from an ecological standpoint: hotter climates will positively impact some species (including species which don't even exist yet!), while negatively impacting others.

The worry isn't that global warming will be bad for animals, you're right, there will be winners and losers, likely in comparable amounts. The worry is that it will be bad for biodiversity, a resource that is extremely slow to replenish (even taking into account these new opportunities). On the edges of the curve, some animals will be huge winners, and some will be huge losers. 10xing the populations of some species while others go extinct is only a net null on the very surface, it's still a huge loss diversity wise.