I understand that Katniss left Gale, but why did she let him go so abruptly?
Katniss believes Gale's bomb killed her sister and she will never be able to forgive him or forget that.
More details / evidence:
Near the climax of the story:
Double bombs go off, first killing targeted victims, then targeting rescue workers, Primrose among them.
Katniss remembers where she first learned of this tactic:
"Im in Special Weaponry back in 13 with Gale and Beetee. Looking at the designs based on Gales traps. That played on human sympathies. The first bomb killed the victims. The second, the rescuerers. Remembering Gale's words.
Katniss believes that the rebels, not the Capitol was the cause:
Those double exploding bombs. It's not that the Capitol couldn't have the same weapon, it's just that I'm sure the rebels did. Gale and Beetee's brain child.
She thinks Gale was involved:
What could I say, how could I phrase it, without implying that it was his bomb that killed Prim?....I finally just say it "Was it your bomb?"
Katniss and Gale both know she will not be able to forgive Gale:
"Was it your bomb?"..."I don't know. Neither does Beetee. Does it matter? You'll always be thinking about it." 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 her, feel the heat of the flames. And I will never be able to separate that moment from Gale. My silence is my answer.....Forgive him. But since I can't, I'll just have to deal with the pain.
Katniss learns about herself that what she needs emotionally, only Peeta can provide. Gale's actions further demonstrate this:
What I need to survive is not Gale's fire, kindled with rage and hatred. I have plenty of that fire myself. What I need is the dandelion in the spring. 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.