Colonizing mars for humanity survival makes no sense for a simple reason

I fully support colonizing mars and I completely agree with Stephen Hawking's prediction that humanity will either reach for the stars or go extinct, but terraforming mars is dumb for a simple reason.

If earth happens to become hostile to life for any natural reason, like climate change and not a comet impact, terraforming mars to inhabit it makes no sense simply because if we can terraform mars we can "terraform earth" (sounds redundant).

Earth can become hostile to life, but mars is currently hostile to life and have been for millions of years, if we could make mars livable it makes no sense why we couldn't make the same to earth. It makes no sense that it would be easier to colonize a lifeless planet over fixing a current planet where all known life forms currently reside.

Again, I fully support reaching for the stars and dreaming big, but why can't earth be part of the "dreaming big" plans? It is nonsense to think "well, we screwed things here, let's literally change a whole other planet and live there instead of fixing stuff here".

Of course, in the case of a meteor impact the perspective changes and there is not much we can do, so yes, colonizing other planets is probably an option that would make sense, but for natural causes, it doesn't.