Well the assumption is that the undeveloped world will
a): always be undeveloped
b): always be overpopulated
If either of those is not the case, then it does, to a degree, mitigate the other. Plus there's always the possibility of heavy handed population control tactics (which have been tried, but not successfully).
Survival, as I've stated, is kind of a tough one, mainly because most people just cannot think long-term and/or for the entire species. If presented with the argument that "we need to invest trillions of dollars into space colonization because we have to deal with future survival that includes the sun expanding (in billions of years, a certainty) and/or an asteroid slamming into us" I feel most people would be like "that seems utterly pointless considering the more pressing problems right now". In the future? It could happen.
In terms of resources, there is one resource that I can see being mined, and that's helium 4 (I believe it may be another one) that's needed for fusion reactors. There isn't a ton on Earth, and there's much more in abundance in space. That is the one resource reason I can see an expansion to space, mainly because even if we use robots to mine, someone's got to maintain them (as of right now), and there would be good reasons to set up more infrastructure for mining.
I can definitely believe the "because we can" argument of going to space being the most viable one. Eccentric billionaires like Elon Musk are certainly trying to push for that.
Here's another interesting reason that I think could potentially lead to space expansion (and is worth debating): alien contact. I feel like that if there was a certainty that alien sentient life existed, that would be reason enough to head out to space and expand a bit for things like trade, etc.