In our eyes, Mitch is so passionate about this because he's closer to Mark. Mitch and Mark probably hung out a fair bit: after all, Mitch in charge of the Ares 3 mission. Teddy might be able to detach himself from the situation emotionally, but Mitch doesn't have that luxury.

Super-friends to the rescue! See, NASA knows that the crew will jump at the possibility to aid in Mark's rescue—as we see later, they'll do it even without NASA's approval. Their friend is stuck on that lifeless rock, for Pete's sake, and they won't let anything stand in their way.

That's the Mark Watney that we know and love. When faced with terrifying, life-threatening situations, Mark doesn't crack up—he cracks wise. He might be losing his mind on the inside, but he's always careful to project positive vibes. In other words, he's a true mensch.