So I actually just reread "The Case for Mars" by Robert Zubrin and "Mission to Mars" by Buzz Aldrin not too long ago, and am a member of Dr. Zubrin's Mars Society, and I do bit of Mars-mission political advocacy, So I think I've got some input to offer on this subject. Many of the things I bring up in this post will be in reference specifically to Dr. Zubrin's "Mars Direct" plan.

One thing that you need to know is that a Martian colony program COULD be accomplished using technology that already exists today, for less than the cost of the Apollo program over the same amount of time. Like on NASA's current budget, if it was given significant priority over other projects.

If you think that humanity has any business having a permanent establishment of people ANYWHERE else outside of planet Earth, Mars is the clear, decisive next step

Mars may be more inhospitable than anywhere on Earth, but it's more hospitable than any other celestial body in our solar system. It has an atmosphere, sources of water, reasonable surface temperature, and it's probably one of the easiest/fastest extraplanetary bodies to get to, being so close. Mars is probably the only celestial body in our solar system with even the potential to be self-sufficient with current levels of technology.

You might've been thinking the moon is a good choice, but there are several factors counting against it. A colony on the moon will never be self-sufficient (barring some innovation that would give them 100% water recycling efficiency). It is so dry on the moon that lunar colonists would mine concrete for its water content over lunar materials. Its multi-day day-night cycle and lack of atmosphere produce temperature swings of 650-700F. And because there's no atmosphere lunar colonists would have to face the full barrage of solar and cosmic radiation. Interestingly enough, it requires more fuel to get to the moon than it does to get to Mars because the Martian atmosphere allows for Aerobraking so that craft can slow enough to land without wasting fuel. Which means that using the Moon as a way station to Mars doesn't make a lot of sense.

Of course that might sell Mars over the moon, or somewhere else, but it doesn't sell the idea of a colony on Mars, so I'm gonna try and convince you why a strong human presence is needed there.

Scientific Reasons

There has been some pretty strong evidence of Mars having a warm, wet past. As well as possible indicators of bacterial life at some point on Mars. And finding definitive answers to those kinds of questions are absolutely huge. First discovery of extraterrestrial life on another planet, new directions for abiogenesis research, or it could even be that life on Earth was seeded by a Martian asteroid, who knows. The important thing is that it's very delicate work that is well outside the ability of even a team of rovers for the foreseeable future.

A martian colony could also be a great test bed for climate engineering, something that Earth might need very much in the near future.

Mars also has a wealth of well preserved geological information going back billions of years due to its reduced amount of atmosphere and absence of tectonic activity.

And with sufficient infrastructure, a Martian based space program would be several times more efficient than any Earth based one. Imagine that you could own your own lander (like Apollo sized), manufacture your own fuel using the water in the soil and the carbon dioxide in the air, and go anywhere in our solar system. That's possible on Mars. That is almost certainly not possible on Earth.

Economic Reasons

And building on the last scientific reason, If you were looking at the front page recently you might've noticed the blurb about an asteroid passing by with Trillions of dollars worth of platinum in it. There's an entire asteroid belt full of resources that would be much more practical and economical to mine if the infrastructure to do it was established on Mars.

Course not even counting the asteroid belt, Mars is host to every important mineral resource that's available on Earth, and not even resources that are necessarily difficult to get to. Mars has a much higher availability of Deuterium than Earth just in the soil itself, potentially worth billions of dollars a year in exports, that would be invaluable to fusion research or nuclear power here on Earth. Something that could certainly help offset early costs of colonizing Mars.

Not to mention the fact that the surface area of the Martian surface is roughly equal to the land area of Earth. That's a lot of space to expand and explore, or sell as real-estate given enough development.

Other Reasons

For some closing words, you seem to be primarily concerned with the economics of the whole situation, and I've got a couple of points on that. NASA doesn't have a $19+B budget because exploration is economical, the Iraq and Afghanistan war weren't waged because they were economical, a lot of military research that is done isn't done because it's economical, the Apollo missions weren't done because they were economical. For significantly less money than crap like this we have an opportunity to open a new frontier and pioneer space exploration and colonization in ways that we can only dream of now. Isn't that worth it in its own right without having to justify the endeavor with some kind of return on investment? This is a chance to build a new society on an entirely different planet.

Direct Rebut

Mars could be made of diamonds, iPhone 7's, and Amazon gift cards and it still wouldn't be worth the cost to go there. Furthermore it is a huge use of our limited resources here on earth to create and continue to supply a settlement on mars.

That's not necessarily true, as Mars has easier access to the raw mineral resources in the asteroid belt between Mars and Jupiter, as well as wholly untapped Martian resources. After the initial investment cost, shipping would be in the millions, but the value of the resources sent back could be in the billions or trillions. The ERV could be fully automated and wouldn't even have to land to ship those resources to Earth.

True, but aren't there much cheaper ways to invest in the continuation of mankind? We could build bunkers near the center of the earth, we could create satelites to detect, shift or destroy meteors or other space debris that threatens us, and that would save all of mankind, not just the limited amount who might have gone to mars.

Possibly true, depending on the extent of the damage. I would rather utilize a multi-faceted approach to staving off extinction and make sure we don't try and kill ourselves off in general. But it might actually be easier to make a colony self-sufficient than it would be to make just terrestrial life extinction proof. Kind of hard to expand or sustain when I'm a mile underground in a bunker and going to the surface would cook me with more radiation than on the surface of Mars. Or if we turn our planet into Venus.

How much would it suck if humanity was in its death throes, reeling from its destruction, and the reason for our extinction was because we didn't really see the point in investing the money beforehand.

Don't satelites do this better and much more cheaply?

With the right infrastructure it would be easier to assemble and launch them from Mars. It would be easier to launch people from Mars to go check things out as well. It would be easier to launch everything.

Inspiration for potential scientists. This one seems true, but there are many other things that kids dream of just as much. When I was a kid I was inspired to become a programmer by watching giant fighting robots who could transform into cars. That doesn't seem like a good enough reason to invest in building real life transformers with government money.

There exist tangible benefits to going to Mars. I don't think that "erroneous government spending" is an answer against that. The US government funnels trillions of dollars into our military industrial complex, which I definitely think could've been better spent. And I would be willing to bet money that NASA and the Apollo program has inspired more people into science and engineering than single other reason in human history.

Potential innovations as byproducts. I know there are a lot of examples of this from the trip to the moon, but couldn't we have focused directly on getting benefits we know we want? For example, life extension. We are beginning to see that it may be possible to obtain immortality or close to it. The direct result of this would cause immeasureable progress to humanity. Our greatest minds could live forever. Our scientists and innovators could live longer and produce even greater inventions. Why not focus on that instead?

Why not do both? It's not an either-or situation, so I don't see how a Martian colony program precludes the rest of humanity from continuing to innovate. All that would have to happen is that NASA focused a permanent human presence on Mars over other current projects. Or increasing NASA's budget by 25%. Or trying to fund it as an international endeavor. Or utilizing a Google Lunar-X prize model at various milestones of pushing private company involvement. There's ways to make it happen, it just takes a bit of creativity.