Mitch Henderson is the closest thing The Martian has to Han Solo. While Teddy and Venkat tend to play it safe, Mitch is bold and brash in the pursuit of what he believes is right. You might dislike his methods, but you can't argue with the results.
Even if you like Mitch, you have to agree with Teddy that the guy can be "a pain in the ass" at times (19.60). The guy is passionate about his work and blunt with his opinions, which is great for getting things done... but less great for creating a good work environment.
The dispute between Teddy and Mitch carries throughout the novel. Mitch frequently accuses Teddy of being "'on damage control'" and "hanging [Mark] out to dry" in a super hostile manner (16.196, 200). Though it's hard to disagree with what he says, there are much better ways to make these opinions known. On the other hand, maybe that's the only way things get done in a big organization like NASA. After all, Hermes only returns to Mars because Mitch goes behind Teddy's back to send them the Purnell Maneuver.
In the end, it becomes clear that Mitch fights so hard because he is the one in charge of the Ares 3 mission. Teddy and Venkat feel bad about what happened, of course, but Mitch feels responsible. When you combine these feelings with Mitch's natural bone-headedness, then can best believe you'll end up with a few cracked skulls.