If we colonize mars, and reach the point where we have a full fledged society there it can act as a means of quickly recovering from a catastrophe on earth. The benefit of a fully functioning city/nation sending resources to assist a ravaged earth would boost earths recovery time if the worst were to happen.
Secondly, it acts as a separate bed of innovation. On earth we solve for earth problems, on mars they would solve for different problems, potentially leading to scientific and tech breakthroughs we would otherwise overlook.
Secondly, it acts as a separate bed of innovation. On earth we solve for earth problems, on mars they would solve for different problems, potentially leading to scientific and tech breakthroughs we would otherwise overlook.