First, Katniss doesn't need an emotional connection because that makes her ultimate goal of survival harder. She recalls how Peeta saved her once with some burned bread, and she feels on some level that she owes him for this. Katniss is known for her calculated and insightful decision-making skills, and an emotional bond with Peeta impairs her ability to make rational decisions. Making decisions with her heart is not in her own best interests.
Second, they both realize that there can be only one winner in the Games. As they survive one day after another, they come closer to an eventual and crucial possibility: Will they be forced to kill each other in the end? While they can survive better together, sharing supplies and lending some emotional support in the midst of the daily chaos of escaping a murderous pack of fellow Tributes, ultimately being a pair is a handicap.
Finally, Katniss has an incredibly close relationship with Gale back in District 12. They have spent years helping each other's families survive. They share common interests such as hunting and archery and there is some romantic possibility between them. As Katniss grows closer to Peeta, she also often remembers the support of Gale back at home. Gale has given her tips for survival in the Games and has even offered to run away with her. Katniss eventually comes to love both Peeta and Gale, and the proclamation of a pair of winners in the Hunger Games means that this conflict will continue after the victors return home.