A few points
For those saying effectively "well we colonised America, how hard can it be?" I could point out that America (and Australia for another example) were already populated by humans when the modern invaders arrived.
There were abundant supplies of food and water and plenty of raw materials to build shelters and the climate was agreeable for most of the year.
Survival required little more than basic tools to get started, although you did need some survival knowledge and tool making and agricultural skills would help (remarkably lacking in a lot of early expeditions I read).
Those talking about masses of people moving off Earth. This is not the most fuel efficient way to populate a new planet. Far more efficient to move well engineered production facilities out and replicate humans on site. Ovaries and testes are remarkably compact compared to the finished product and you can screen for (in your view) desirable traits in the producers. Compare this to our planet where the "bangs per buck" made it cost effective to move humans in bulk to provide labour in the colonies. Hence prisoners and slaves.
The poor aren't going to get a look in either. The high cost of shipping humans to orbit and beyond and sustaining them will almost certainly lead to an indentured elite living off Earth under conditions dictated by the financiers who provided the transport and accomodation.
So for the race overall it makes sense to move off planet and spread the risk. For all but a vanishingly small minority it will make no difference. We are stuck on this polluted mud ball and so are our descendants.
The planet will most likely survive in some form whatever hits it. It has so far. Life will also survive, although not as we know it (Jim). Humanity is a fly speck on the timeline of Earth.
Anyway, go Elon. Humanity needs to infect the Universe before this local infestation gets sterilised.