There is a real difference between a singular event like an asteroid, and a slowly boiling frog like climate change.
You can point at an asteroid and say "That thing. It's going to melt half the planet." I'd like to think we could collectively get our shit together and find a way to fix that.
But climate change is more insidious because it's so slow. It's in every nations best (short term) interest to ignore climate change. And there are zero short-term consequences to politicians because the average person probably won't measurably see an effect in their lifetime. Sure, summers might get a bit hotter and have worse floods, winters get a bit colder. New pests will pop up, species might start to die. But there's not a galvanizing event to really scare the shit out of people. Even if people believe climate change, they'll shrug, tsk tsk a little (like I'm doing!), maybe stop using plastic bags or install solar on their house or something. But it's negligible, and they know it's a meaningless gesture because everyone else has to make the same gesture for it to work.
Eventually it'll get bad enough -- widespread fires, droughts, rampant pest or diseases, all the pollinators die out, whatever -- that people really start to take things seriously. But by that time we might have 20 billion humans on the brink of starvation and it'll be a bit late to do much more than try to survive.
I doubt humans will ever go extinct completely. We're pretty hardy primates. But it's very possible we get knocked back to hunter/gather tribes (probably with some neat technology!) scraping a living in some kind of post-apocalyptic industrial nightmare.