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You can't really believe that; certainly Musk doesn't. Edit: Just for one challenge with no current solution: http://www.nature.com/articles/srep34774 There are others.
Why not? And what makes you think Elon doesn't?
He's positioned for LEO cargo, and in the longer-term (I suspect) for potentially surveying and mining asteroids. There is almost literally money out there, for the first people to stake a claim. It's daring, it's risky, but it's possible to do with a combination of human explorers and robotics.
It's not sexy however, and it calls to mind all of the dystopian sci-fi of the last few decades. "We're going to Mars folks!" is just... easier to swallow than... mining space rocks.
People like you and me want to believe in a secure future for the species, which requires getting a self-sustaining group of humans off this planet. It's a powerful dream that could really move some very bright and dedicated people, who might not be similarly moved by the dream of simply gathering more resources for Earth.
Elon Musk, I think, has perfectly blended PR and a real business plan, but the PR and plan are not one and the same. More credit to him, but it's a bit discouraging to see so many people flip the switch on their skepticism out of pure "wanting it to be true".