I think humanity moving into space will fail (well, Earth is in space, but you know what I mean), because we're lacking in good reasons.
I read scientists saying "it isn't a wise thing to keep all the eggs in one basket", if something happens to Earth, humanity will be done. But who the fuck actually cares about this? It's wise thing to say, but hard to make it into a personal motivation to support moving into space. People themselves personally want to be safe, that's what they can understand, "who the fuck cares about humanity if I or my loved ones die?", they would want an option to flee if shit happens, and don't think about such bs, like "preserving humanity". It's just too abstract for us, and to be honest due to living things' "selfishness", preserving humanity starts with preserving ourselves.
No doubt there are altruistic people, and people who would want to conserve more than just humanity, other species in huge numbers would be fucked, and some people have Noah complex too. But they are just an insignificant part of humanity.
The other chief reason I see reoccurring is the abundance of resources in space. Giant rocks orbiting in our solar system with all kinds of usable materials, from water to metals, even rare elements in huge amount (compared what we have on Earth). But reaching those resources would mean giant effort, time, work, capital thrown into it, and would cost great amount of said resources extracted on Earth which could be spent otherwise. And when we reach them, then what? They need to be extracted and process, we need places to utilize them. Foundries and whatnot. And brought back down the well, since here on Earth we'll need them. Unless we move most people out somewhere. The whole thing sounds extremely unfeasible, and exactly the type of thing Rusbernd wrote: private firms won't touch it but wait until govt finance it. But governments are swamped enough with filling potholes of poorly constructed roads. No.