Gale + Katniss
Like Katniss, Gale is a hunter. He's most comfortable when he's out looking for game. He and Katniss have a history together. Before the Games, before the Quell, before it all started, Katniss and Gale were a team. They were the best of friends and relied on each other to keep their families safe. If Katniss hadn't ended up going to the Games, she "wonder[s] what would have happened to them […] if she would have fallen in love with the boy, married him even" (26.29).
Gale – Katniss
Gale and Katniss could have had a different future together, in some ways harder and in some ways easier than the one we see them living in Mockingjay. But circumstances got in the way. In some ways, as soon as Katniss went off to the Games, Gale knew he was fighting a losing battle for her affection. At one point, Gale admits to Peeta, "The way she kissed you in the Quarter Quell... well, she never kissed me like that" (23.84). Maybe on some level, Gale's always known he couldn't compete with Peeta.
Part of the reason why is that Gale's hunting instincts make him start to depersonalize people. We can see this in the scene where Katniss realizes exactly what kind of weapon he's created, along with Beetee:
This is what [Gale and Beetee] have been doing. Taking the fundamental ideas behind Gale's traps and adapting them to weapons against humans. Bombs mostly. It's less about the mechanics of the traps than the psychology behind them. […] Luring the victim to a safe haven – where death awaits them. At some point Gale and Beetee left the wilderness behind and focused on more human impulses. Like compassion. A bomb explodes. Time is allowed for people to rush to the aid of the wounded. Then a second, more powerful bomb kills them as well. (13.41)
It turns out this quality has ruined Gale for Katniss. She can't stop thinking about this aspect of his personality after Prim dies, even when she's sitting down with her formerly worst enemy:
I'm not with Snow now. I'm in Special Weaponry back in 13 with Gale and Beetee. Looking at the designs based on Gale's traps. That played on human sympathies. The first bomb killed the victims. The second, the rescuers. (25.40)
Ultimately, this is what drives a wedge between Gale and Katniss and keeps them from being together. It's what helps show Katniss that Gale isn't focused on life, but on vengeance. It's not, ultimately, about whether it was his weapon working that killed Prim or not; it's that he was willing to invent it in the first place. The fact that he did so has helped create a "dark, twisted sadness between them" (26.29).
Towards the end of the book, Katniss finally gets up the courage to ask, "Was it your bomb?" (26.33). Gale's response is, "I don't know. […] Does it matter? You'll always be thinking about it" (26.34). And he's right.
Gale's a good-looking, telegenic, intelligent warrior who got plenty of press during the war. It seems clear he'll land on his feet. But by losing Katniss, what else might he be giving up?