Haymitch promised her that he would tried to win, for her. Haymitch saw the same thing in Katniss and Peeta as he saw in himself and Maysilee. He couldn't see them experiences the same things he had to, for he cared for them too much.
He cared for them too much. That's why he convinced Seneca Crane to bend the rules for them.
Haymitch drinks so much because the loss of Maysilee was too much to handle sober. He spends most of his time at the bar or drinking.
On the train back to the Capitol with Effie, he, like usual, spent most of his time in the bar car, drinking.
He sat on the barstool, very drunk. Effie walked in and sat down next to him. Before he knew it, he was leaning over, vomiting on Effie's shoes, which, in his opinion, already looked like vomit.
She stormed off, leaving him with his disgusting vomit.
She returned to the bar about an hour later, tripping over her own two feet.
"Haymitch, I..I..I like you."
"What?" Haymitch thought. "She LIKES me?" Haymitch hadn't even considered that Effie would have those kind of feelings for anyone, especially him. It was obvious that Effie was not even close to being sober, so he thought that it was the alcohol talking "Well," Haymitch started. He didn't want Effie to like him. He was too disgusted with himself to let her love him. "If We're making confessions here, I don't really like you.
Haymitch regreted saying that to Effie for the rest of his life.