Answer by Alex Guerra:
The most succinct answer to this question is: climate change is bad because evolution is slow.
It takes millions of years for species to adapt to specific environmental conditions. The slower an organism's reproductive rate, the slower the rate of adaptation an organism will experience. The more specialized an organism is, the less able it will be to deal with a variety of situations. Organisms have spent millenia adapting to the current climates in regions world-wide.
The biggest problem that we will face is that if the climate starts to rapidly change, it will outpace the rate at which organisms can adapt to it.
In other words, if the climate starts changing rapidly in one region, it can easily drive local populations to extinction because their ability to tolerate the new physical conditions will not be able to keep pace with the rate at which the physical conditions keep changing. Now imagine the same thing, but on a global scale where every local climate is shifting rapidly enough that local populations are dying out.
The greatest danger to humanity from climate change, is the extinction of most life on this planet in a short period of time. An event such as this would make it near impossible for humans to survive. Think about what would happen if plants globally went extinct, including agriculturally important ones. And herd animals. And bees and other plant pollinators. Even if you were to move elsewhere to a new climate that could support agriculture, you'd be at risk that the climate would change again before you could effectively grow crops, and you'd have to manually pollinate plants due to a lack of pollinating insects.
It's a doomsday situation that warrants global attention.