I think what bothers snow the most about both haymitch and katniss' relationships is that THESE versions of the covery girl/loverboy actually STICK together. He tried to justify his actions by telling himself that it wouldn't have made a difference, that Lucy Gray did not actually love him, acted as if the love wasn't there so something had to change (and he made that happen). But both Haymitch and Katniss show that the love DOES make a difference even by just being there, not even in a romantic way (i absolutely HATE the way people try to make a Maisilee x Haymitch ship and not let them be platonic. I see them as siblings purely. Not every male/female dynamic is romantic and not everything is about the romantic love story for fuck's sake. ) but in the way it connects people, even when it isn't there it turns to creed. These people can be robbed of A LOT yet keep some faith and get going. Something snow was NOT able to. It mirrors the excuses he made for himself. It shows him his failure and how it was the first step in his career. A failure that lead to his glory. But imagine the shame it brought upon him if people knew that, right?
It's almost as if he's got imposter syndrome, except he actually is the imposter.
And the way these two work is also that it is never ONLY about the person they love most, significant other blablabla - there are always other things [for example the Revolution but also smaller things like hunting, baking, painting, etc etc] that matter and it's okay because people have more than one interest yet the love for their people who have nothing to do with that thing is STILL there and it ALL matters.
It shows Snow a freedom he doesn't understand with his obsessive tendencies, family dynamics that aren't about keepinh the family name clean shows that people value different kinds of honor, and all of that is what crumbles his structure. The belief system he had built and always looked down upon on other people.
Because he was a young guy with self esteem issues and his way of fixing it was just getting rich and powerful, believing in the system.
But THEIR way of dealing with hardhships just like his, was giving each other strength, not hiding their lost net value. They keep it raw despite all of that yet no one leaves the other for it (one of snow's biggest fears) or shames them for it. The Revolution is so dangerous to him because it makes him face his belief system, all that shaped him, and his old feelings that never really vanished.
"It's the things we love most that destroy us" - and for snow that's CONTROL. And these people show him that there are other things they value more than that, more than his control but also more than their own control because the districts pretty much grew up without any of that. They make it work without what he thought is the source of panem.
