It goes beyond just climate change. No matter what Earth will be uninhabitable at some point. The vast majority of the history of life on this planet is in the past. The Sun is getting warmer over time. In 300 million years the Earth will be 5 degrees Celcius warmer just from direct sunlight alone and 15 degrees in a billion years and the oceans will boil away soon after. While it varies, it is hypothesized that multi-cellular life will be unable to survive on the planet anywhere from 200 million to 800 million years from now.
And that's just what's certain. There are still things like asteroid/comet impacts, supervolcanos (it is believed that the Toba eruption 74000 years ago nearly wiped out the entire human race), nuclear war, etc. that could devastate the Earth.
If humanity is to survive, we need to get off this planet (and eventually out of the Solar System), end of story.