Why?
Were scientists only kidding all these years about the atmosphere and climate of Mars?
Is it really actually breathable, warm, and has running water?
Here's why:
Have you heard of the overpopulation problem on Earth? Is the solution to go the route China went and have governemnt control our reproduction? Talk about lack of choice. Do we just execute more people, again this involves a great amount of government control over who lives and dies. Do we just let things run their course and deal with the food shortages and the mass poverty? I'm sure the riots will help us get the popultation back under control.
Then there's the problem of our existing economic model of infinite expansion. That doesn't work forever here on a single planet, but seems to fit in quite well considering the size of the universe. Again, to solve this problem on earth requires governemnt to force a solution that will not be in everyone's best interests.
Then there's the problem of differeing religious/cultural views that are causing never-ending tensions throughout the world. If only the people who find the way other people live as unaceptable could go their own way and to their own place.
Then there's the less tangible aspect of the human "spirit." Adventure and discovery seem to be beneficial to the human outlook. The idea of the freedom of the frontier.
As mentioned, the long-term survival of our species looks a lot better when all our eggs are not in one basket. A meteor, a "super-valcano", nuclear war, etc. could wipe us out and end what as far as we know is the only intelligent life in the Universe.
There's a lot of learning to do. Learning how the best way to travel from planet to planet. Learning how to survive on other planets. Learning how to get resources from one planet to another. These are all things we can take baby steps on because we've got the moon to act as our training wheels for our earliest endevors into space and Mars as a near-by target for our first attempts at actually living on another world. It is almost too good to be true, yet we question the value of even gaining the experience.
I'm not sure that if we don't go to other planets that it will directly mean that we cure cancer or feed the hungry or give every child a good education. All I can say is that 5000 years from now we'll be a pretty sorry species if we're still trying to cram all of our sorry asses onto Earth.