Compelling reasons: well, for starters, that colony would be insurance against an extinction-level asteroid impact here on Earth. So there's that.
I think wanting Mars-tronauts to be "productive" and whinging about the cost and the "enormous expense of keeping them alive" somewhat disqualifies you from this conversation.
I believe that we absolutely should and must continue exploring the universe, continue with probes, satellites and occasionally maned space flight. However the idea of manifest destiny is purely ego. The universe doesn't need us. It won't miss us when we are gone whether we populated one planet or a trillion.
Our advancement and betterment is for our benefit alone. I can't really see how throwing ourselves off the planet on chemical rockets to live in tin cans leads to the betterment of anybody. It takes time, resources and energy from sciences that could have vastly greater long term benefits. Yes, it might help us get a head start on future engineering hurdles, and helps improve public interest, but frankly, the really interesting stuff is going to be happening down here on earth for a good while longer. If we bite it as a race, so what? If we don't, then we have only the benefits of our long-term investments to reap.