Imagine you were born in a deep well. Even though the bottom of the well contains everything you need to survive, you have always looked up and dreamed of escaping. Finally, after years of effort you manage to painfully claw your way out. After escaping the well, what you don’t do is look for a worse well to fall down. This is, in short, why colonizing Mars is a silly idea.
I support humans traveling to Mars for science, but colonizing it or trying to terraform it doesn’t make sense. Even though the idea is very popular in science fiction and has some big name support, like Elon Musk and Stephen Hawking, it has four big problems.
1) Mars is cold, dead and far away - The Earth has free air, warmth, and sources of food. Space stations at least have free power from 24-hour solar energy. Mars, on the other hand, has almost nothing going for it. There is very little atmosphere, the planet is cold, and there isn’t an ecosystem that would be of use to us. While Mars has water and other basic chemicals, the same is true of many asteroids. Mars is far from the Sun, the main source of potential power in the solar system. It receives less than half of the solar energy the Earth does. Mars is also far from the Earth, making it difficult to get anything to Mars or for anything to get back from Mars. This means any Mars colony would be a pure economic drain.
2) Contamination - We don’t yet know if there is life on Mars, but there is a really chance some might exist. If there is indigenous Martian bacteria or mold, any attempt at colonize or terraform the planet could easily destroy these potential lifeforms. That would be an almost unparrelled scientific tragedy.
3) Disaster of the commons - Terraforming Mars would create an incredible number of political/social/economic issues. Terraforming would be an expensive, long-term investment. It would be very difficult to decide who pays and who would benefit. Does anyone get to live on Mars after it is terraformed, or only people from countries/companies that paid for it? There is also the question of when to stop. Who decides to raise or lower the sea level making huge stretches of land disappear?
4) Gravity - Mars might be a reverse Goldilock -- it potentially suffers from being both too big and too small. The gravity on Mars is roughly 38 percent that of the Earth. That is high enough that it still takes a significant amount of energy to lift anything off the planet, but it could still be low enough that it could cause significant health issues. We know weightlessness causes a host of health problems for astronauts and interferes with embryonic development. How much gravity is necessary for good long-term health is an unanswered question. Martian gravity might or might not be enough to meet our needs.
Asteroids are much better alternatives
On basically every level asteroids are simply a better potential new home for humanity. We can find/bring decent-sized asteroids much closer to Earth and closer to the sun, our best potential source of energy. These asteroids could be used as a source of raw material to bring back to Earth or to build large space stations with. By mining these asteroids for precious metals that could be shipped back to Earth, we could potentially create a legitimate economic reason to start a colony in space. It would be a mutually beneficial arrangement between the colonists and those on Earth, instead of a pure economic drain.
It is unlikely that asteroids contain any indigenous life, so there are no real contamination concerns.
Turning an asteroid near Earth into a decent-sized space station would be a significant investment but still less than colonizing Mars. It could also be done faster than it would take to terraform a whole planet. By going with this smaller approach, there would be fewer political/economic issues.
Finally, you can easily spin a space station to create whatever level of gravity you need. You won’t need to worry about the health problems low gravity might cause, and you don’t need to worry about building rockets powerful enough to escape a planet's gravity well.
There are strong arguments for starting off-Earth colonies. We don’t want to put all our eggs in one basket and risk a mass extinction event, but that doesn’t automatically mean colonizing Mars is a good idea. There is much better real estate out there.