>

Why would there necessarily be more testing on Mars than on Earth? Any project on Mars is going to be orders of magnitude more expensive than a comparably sized project on Earth, so that would suggest less money for testing (given a similar budget).  
Why would mineral resources be easier to obtain on Mars than in Antarctica? Though much of the continent is covered in icefields, there are large dry areas (Antarctic oasis) which are essentially like the surface of Mars but with an atmosphere and magnetosphere. Metal and mineral resource would presumably be available in these areas.  
It's true in Antarctica you wouldn't have much solar potential, but there is ample wind power available. There are also coal deposits.
I feel like the only way Mars is better is if you are assuming that we will be willing to pay way more to set up a Mars colony, or that such a colony would have some way of being economically viable in a way that an Antarctic bunker colony could not.
We haven't sent anyone to Mars yet, that's just the long term goal and probably won't take place until we get more infrastructure up into space and the moon.
Rockets do emit carbon dioxide but there are so few of them that it won't make a huge difference, especially in comparison to all the other options for lowering carbon emissions that we have. >

To expand on the second point:
A single ~~average sized~~ large international airport causes more CO2 emissions in a day than every rocket launch on earth for an entire year. >

that makes no sense. source please. >

And rockets launch communication, broadcast and GPS satellites, without which our global shipping industry would also very much collapse.
They also launch weather satellites enabling us to better predict things like hurricanes, or allow us to detect wild fires early.
Research for Space applications has led to countless spin off technologies that make our daily lives possible. >

When the entirety of the human race is confined to one planet, then all it's takes is one astronomical event to wipe it out. If humans are to persist and survive, they need to eventually colonize other planets.
Mars is the easiest place to attempt it first. >

If human's were to build a self sufficient bunker in a remote location on Earth (say Antarctica) which made it's own food, oxygen, energy, material resources, etc. and had a population sufficient to repopulate the earth without inbreeding, what astronomical event couldn't it be designed to survive? Certainly building such a bunker would be far cheaper than a Mars colony. >


what astronomical event couldn't it be designed to survive?

A large enough meteorite impact, for instance. >

Are there any known asteroids/comets with an orbit that could theoretically intersect Earth's that would be so large that a bunker could not be designed to survive the impact? Clearly something the size of the asteroid that caused the K-T extinction (end of the dinosaurs) wouldn't be sufficient, since plenty of species survived so presumably people in a well built bunker would be fine (assuming we are not so unlucky so as to have the object impact directly on the bunker, maybe that is an argument for building 2). >


Are there any known asteroids/comets with an orbit that could theoretically intersect Earth's that would be so large that a bunker could not be designed to survive the impact?

No... we're not talking about the coming decades here, not even the coming centuries. We're talking about a fundamental mechanism of security for the next milennia, maybe beyond. It's not likely that anything of that scale will happen, but it is certainly a good idea to work towards the necessary technology while we can.

presumably people in a well built bunker would be fine

I think you're imagining this a little too optimistically. There is more to the whole thing than just surviving the impact - you need to have a somewhat stable society, enough genetic diversity, enough material and know-how, plenty of energy and the ability to function without any outside interference. 
"It's the same for Mars!", I can hear you say - but there is one fundamental difference: this bunker would likely be used when it is needed. A colony on mars could grow in relative isolation for a very long time before a cutoff would happen, allowing for a much greater possibility of relative stability - or otherwise, a retry. I would even say that life on Mars would be significantly easier than life on post-extinction-event earth, especially with potential decade-long ice ages that make any sort of progression and expansion nearly impossible. >

Why would life on Mars be easier than post extinction event Earth? Even after an extinction event Earth would still have more easily available oxygen, water, soil, a magnetosphere, etc. >


Why would life on Mars be easier than post extinction event Earth?

Primarily because you still have access to resources - metals and minerals are easier to find on mars than in antarctica. You also potentially have a greater ability to expand and most likely a much greater potential for gathering energy. In antarctica, you will be mostly limited to geothermal energy, whereas you can fall back to solar energy on Mars.
Key point is: Mars can be tested and problems fixed - in the bunker scenario, there is most likely not much testing, especially under real conditions.