Does anyone else believe that climate change is just another severe pressure for life to adapt?
Sure, life will go on. But keep in mind that if you view the geological record, swings in climate are generally associated with mass extinctions. So given that, it would seem a lot of species are unable to adapt quickly enough to climate change and simply die out. Your science teacher is assuming there is something special about humans as a species that will allow us to adapt to a different climate by evolving. A more balanced interpretation of the evolution of humans suggests there is nothing special about us in that regard, and our survival is about the same as any other species. Really though, what we care about is not so much the survival of humans as a species but survival of civilization.