Maybe an apt metaphor is with pressure. Go from ten atmospheres of pressure to one in an hour and your ears will pop. Do it in less than a second and your blood vessels will pop.
The problem is that we also like living on this planet, and climate change might make a good portion uninhabitable in my own or my children's lifetime. Also people really like living on the coast, and either relocating them or combating rising sea levels alone will cost a fortune. Not combating climate change is the most expensive decision we can make.
Planet will be fine, we won't.
And no - it won't just be people in 3rd world countries. If that's fine for you then sure. We will be fine.
EU just had a so called "immigration crisis" because a few million refuges came and people disagreed how to deal with them, to the point of populist governments being elected and some countries considering leaving the EU.
Now imagine not 3 millions but 500 millions of refuges. How will the world deal with that? All of this while food is becoming much more expansive, and there is a need for many infrastructural projects to save coastal cities. The likely answer is - political turmoil, mass crimes against humanity, wars, failing states.
The biggest problem with global warming is that people reject solutions because of well-estimated costs, but they don't even try to estimate the cost of not doing anything, and when it's estimated for them they just ignore it like it's not there.
Yes we should do things to make it suck less but to imply that the end result will be a planet with no humans on it is hyperbolic and farcical.