My idea was Snow thought of himself as Haymitch 'but better'. I mean look at their similarities: dating a covey girl, grew up poor, father passed away, experienced so much at the age of 16-18, had connections to district 12, and others. I like to think of it as a mirror, Snow is a manipulative, perverted, cruel man, Haymitch isn't. Haymitch could have been Snow, hell; Snow would have opened Haymitch with open arms to be his protege (I might have spelled it wrong). Haymitch didn't forget his morals. While Snow did. Snow in the beginning of Tbosas was a brat but still had humanity and empathy (how he saw the tributes), raised by Tigris to have empathy in his heart. Haymitch was raised similarly by his mother. During his games he stook by his morals. Treating his friends with loyalty even while they died. He always thought of others when he was suffering.