1. Resources on Earth are limited. Once it's economically viable (and it seems we're going that way), even without actually living in space, we can get stuff from it instead of drilling your beloved Mother Earth till there's nothing left.
2. Space on Earth is limited. Yes, a decently planned arcology system might allow us to house trillions on Earth without suffering hunger. But there'll be no arcologies on Earth in the next few millennia - it requires the scope of planning we as a species are not capable yet. And building the said planet-spanning arcology will require resources and energy from space - we probably don't have enough here.
3. Long-term survivability of Earth is limited. We either establish permanent self-sustaining bases everywhere we can reach as soon as possible - or we'll be fucked by time and space, figuratively. An asteroid might hit one planet or moon, but not another at the same time. Same goes for solar CMEs. Same (but on the scale of solar systems, not planets) goes for GRBs, nearby supernovas, aging of the Sun and so on.
We should solve problems on Earth for sure. But concentrating on Earth ONLY will lead to our downfall. If not in a century, then in a millennia. Not in a millennia - in a million years.
If early humans never left Central Africa - they probably would've been wiped out by the first thing (animal, weather pattern, disease, you name it) they couldn't adapt to rapidly enough. Spreading out allowed us to survive and prosper; and the history will repeat itself again and again.