Quote 28
He waits for me to deny it; I want to deny it, but it's true. Even now I can see the flash that ignites [Prim], feel the heat of the flames. And I will never be able to separate that moment from Gale. My silence is my answer. (26.35)
Let's face it: Katniss's love for Prim supersedes her love for Gale. And the doubt she has about whether Gale contributed to Prim's death is enough to keep him away from her forever. Whatever they had before is lost, because Katniss can't separate him from her understanding of Prim's death and what/who might have caused it.
Quote 29
[…] what I need to survive is not Gale's fire, kindled with rage and hatred. I have plenty of fire myself. What I need is the dandelion in the spring. The bright yellow that means rebirth instead of destruction. The promise that life can go on, no matter how bad our losses. That it can be good again. And only Peeta can give me that. (27.62)
When Katniss finally chooses between Gale and Peeta, she chooses Peeta. In doing so, she chooses peace instead of revenge, nurturing instead of ruining, and "rebirth instead of destruction." Gale would feed her need for revenge and perhaps for power. Peeta helps her to be free of that, and that's part of why she loves him so much.
Quote 30
Gale asked to be dropped off in 12 with me, but he didn't force the issue when I refused his company. He understands I don't want anyone with me today. Not even him. Some walks you have to take alone. (1.9)
Even the greatest, best friends can't be there for you <em>all</em> the time. As close as Katniss and Gale are, he can't stand by her in this moment; she needs to do it by herself. At the same time, she distinguishes between him and the other people she's with in 13. Of all the people there she "do[esn't] want anyone," "not even" Gale. If she would want anyone by her side, though, it sounds like it would be him.