The planet Earth will not be around forever and we need to find alternate places to live. Mars is the first plausible place. As we saw in The Martian with Matt Damon it is possible for someone to survive on Mars. Space is the final frontier and we need to keep exploring it.
Almost all leading cosmologists and future-facing scientists agree that for the future of the human race and for disaster redundancy we must look outside of the planet Earth to support our population growth. Elon Musk is correct in saying that a colony on Mars would be the clear next step to achieve this.
We will never be able to fully solve humanity's problems. Something drastic would have to happen, and should that happen we'd have a greater chance at surviving if we could gain the knowledge, wisdom, and experience of colonizing other planets.
Plus Mars is the Adeptus Mechanicus homeworld, so.... Dibs. Praise unto the Machine God. Glory unto the Omnissiah. May humanity be guided by the Motive Force.
As a long-term goal, extra terrestrial colonization encourages innovative scientific thinking and development of solutions to problems that can also be applied to harsh environments on Earth. Whether it enables people to actually live on Mars, or merely opens up some of the harsher terrain on this planet, it's likely to help human development and survival. It's a great end goal to have, even if it proves to be impossible; and of course, what is impossible at one level of technology may well be entirely feasible after another few cycles of scientific development.
We should not try to colonize Mars until we have learned how to fix the problems we have on Earth first. Humans are unable to live peacefully among ourselves, use our resources wisely or provide everyone's basic needs - like shelter, food and health care - to which everyone has a right. I cannot see any benefit to setting up such an imperfect society in a place where survival would be made much more difficult without even the basics of water and arable soil. If we can't share our abundant resources fairly on Earth, there is not much hope for doing so on an inhospitable planet.