This is because Snow has established complete control over her, using her family as leverage and manipulating her into participating in the Quarter Quell. Katniss knows that any defiance will result in harm to her loved ones, so she complies with Snow's demands, even if she despises him.
While she does have relationships with other characters, like Peeta, Haymitch, and Gale, she is ultimately powerless against Snow's authority and must submit to his commands.