Hmm… how can we describe Katniss and Peeta's relationship with their mentor, Haymitch? We'd have to categorize it as "love/hate." Haymitch got them through the previous Hunger Games (somewhat miraculously), and he's a great strategist, but half the time he's totally out of commission. When he's not drunk, he's on it – but he's drunk a lot of the time.
Haymitch also isn't always open with Katniss and Peeta, pulling stunts like playing them against each other by promising them that he'll work to make the other survive. Katniss and Peeta realize they're caught in "[a] double deal. A double promise. With only Haymitch knowing which one is real" (24.75-76). Not to mention, he keeps them totally in the dark about the rebels, District 13, and the plot to bust the Quarter Quell tributes out of the arena. That's a lot he's kept hidden.
Haymitch is a great mentor if you happen to be stuck in the arena. Although he practices tough love, he watches out for his tributes as best he can. Just before the Quarter Quell started, he even gave Katniss a clue that would end up saving her life in the arena:
"Katniss, when you're in the arena […] You just remember who the enemy is," Haymitch says. "That's all." (26.50)
Haymitch knows "who the enemy is": the Capitol. He's been working for the rebellion all along, maybe in spite of himself. If he didn't have to be a mentor for younger tributes, or have a cause to honor, he'd probably just drink himself into a permanent stupor.
See, Haymitch is also damaged by his past. He won the previous Quarter Quell, the 50th Hunger Games, which was a total bloodbath because it had twice as many players as usual. He won based on a combination of luck and skill, plus the realization that the arena itself could be used as a weapon (something Katniss picks up on later). That's a lot of trauma to experience, and Haymitch is still suffering from it, even though it was 25 years ago. He drinks like a fish and sleeps holding a knife. He has no family or partner. At one point, Katniss says she thinks of him like family, but apart from her and Peeta, he really has no one.
The thing is, suffering through the Hunger Games together forged a bond that will forever hold the three of them close. Katniss will always be loyal to Haymitch:
[Haymitch is] surly, violent, and drunk most of the time. But he did his job – more than his job – because for the first time in history, two tributes were allowed to win. So no matter who Haymitch is, I owe him, too. And that's for always. (1.24)
Katniss owes him even more by the end of Catching Fire, although she's also angry with him for tricking her. Haymitch's only response is that it was for her own good.