Well there are so many assumptions in this question. I don’t think either is necessary, possible yes, but not necessary. We don’t have to have space colonies either, though for a sci. fi. geek it’s a cool idea :).

It’s understandable since we have people like Elon Musk and even Stephen Hawking saying over and over that we have to become a multiplanetary species. But - no we don’t. Even the brightest people sometimes make mistakes and it would be a sad state of affairs if we just accepted anything that someone very bright or very successful tells us without question.

So first, there’s the assumption that our civilization is expanding. If we explore space and send humans to outposts throughout the solar system, it will expand physically. But the population may not expand much over what it is now.

Our world population is still expanding, but the population of many countries has already stabilized and is declining slightly. Fertility levels worldwide are declining, and are often already below replacement. We have reached peak child in the world as a whole, so there are the same number of children this year as there were several years ago. That means our population is now growing only because we are healthier and living longer than previous generations.

Other places will level off towards the middle of this century. The main unknown is Africa - the least developed, poorer countries have the most rapid population growth and most of those are in Africa. So it depends a lot on what happens there, and how rapidly their fertility rate declines. The middle of the road projections have our population level off at 10 billion by 2100.

Space colonies would be even more affluent and high tech than any of these, so in the natural course of events, they probably wouldn’t have an expanding population either - unless there is some political drive for them to have large families, sort of the opposite of the Chinese one child families.

So, we don’t need more space to house people. Anyway we use our Earth quite ineffiiciently. If we used the same technology as is proposed for space habitats, we could feed the entire Earth from 22% of the Sahara desert, using only the air and sea water. If we used it in floating sea colonies - again not hunting the sea life, just floating farms on the surface of the sea we could feed four times the world’s population from 0.5% of the Pacific ocean.

That might be one of the main benefits from space habitats, not that we have lots of people live in space, but that we learnt to live in a more sustainable way.

Also, we don’t need to colonize space to escape natural disasters. Humans as mammals are much better adapted to survive extremes of temperature than the dinosaurs were, especially when you add in the ability to make clothes, and to make boats, travel. Also when you bear in mind that we are omnivores able to eat fruit, nuts, seeds, roots, insects, shellfish, fish, animals, birds. There is no credible natural disaster that would end up with a world with nothing in it that humans could eat. So long as something survives edible, somewhere in the world, we can travel there, cultivate it, farm it or whatever and then some humans will survive. And we can also set up seed banks, and prepare in other ways too.

So the idea of humans going extinct from natural disasters is just absurd if you think it through like that. Some think that the Earth could be destroyed by a giant asteroid - but forget about the movie asteroids hundreds of kilometers in diameter. The Earth hasn’t been hit by anything that big for over three billion years, nor has Mars, or Mercury or the Moon, or what we can see of Venus’s history. Jupiter it seems protects us, diverts the larger comets, or breaks them up or they crash into Jupiter or the Sun.

So, we are just talking about Chicxulub size asteroids, 10 km or so, maybe a bit more. No asteroid that large is on a collision course with Earth and we have mapped all the NEOs of 10 km upwards already. So that only leaves comets and those are very rare, perhaps 1 in 100 million chance of any of those this century and we’d have a year or two of warning.

But anyway, those would not make us extinct. Not humans. Dinosaurs maybe. It’s the same for gamma ray bursts and supernovae.

So that leaves the risk of making ourselves extinct through our technology and discoveries. You can certainly make up a science fiction story where a space colony “saves the day”. But equally you can make up a science fiction story where space colonies actually cause a future disaster. Not at all clear that space colonization actually makes us any safer as a civilization.

Also Earth is far far more habitable than anywhere else in the solar system, for humans. No disaster whether self caused or natural could make Earth less habitable than Mars. So Earth is where you’d want to build in that very remote possibility.

I think our priority has to be to be to protect Earth and help it recover. Space colonization or settlement might help with that, if they are in space doing things that help Earth, e.g. mining, or making solar panels, or indeed making discoveries that help Earth.

So I think it depends a lot why and how we do it.

For more on this, I go into a lot more detail, see my Wait, Let's Not Rush To Be Multiplanetary Or Interstellar - A Comment On Elon Musk's Vision

Also my book (which has that as one of its chapters): If You Love Science, Don't Rush to Land or Crash on Mars