Let's talk Logistics.
Presume there are only 1 billion people left on Earth when we decide it's time to go. How do you get them there? The gravity well holding us here (and holding the air down so we can breath it) is pretty darn strong. Today we're hoping to get cost-to-orbit down to around $100/kg. I weigh a bit less than 100kg, so that's $10,000 just for my mass- not including the life support system I need.
And then I'm just in orbit.
If I'm moving to some kind of spin-gravity station in orbit, that's not too far away. But Mars? Mars is a months long trip in a best case.
And don't get me started on planets on other stars. Even the most optimistic generation ships would be taking 10s of thousands of years to get there- longer than all of human history so far. If each ship held 100,000 people, you'd need 10,000 of them. And what power source would you use to move that massive ship, and keep the light and heat on between stars? (Antimatter, I guess?)
If we can make Mars habitable, we can make Earth habitable for far less cost.
I'm entirely in favour of building spin-gravity stations, Mars habitats, even terraformation of Mars and Venus. I just feel like it's never going to be the case that anything more than a tiny fraction of humans will leave Earth to go see those things.