Why doesn't Katniss want to get any close to any of the tributes, including Peeta

Katniss knows that, if she wants to win, she will eventually have to kill them. She is not good at making alliances in order to further her own interests. She knows that eventually everybody will be out for themselves.

Katniss doesn't want to get very close to any of the tributes including Peeta since people have a way with her. People have a way to get under her skin and staying there. She's scared that if she and Peeta join, he'll betray her and kill her in her sleep. She also knows that in order to win she needs to kill every single last one of the tributes, including Peeta which means that she can't have any connections with him for the rest of their time in the capitol.

Katniss doesn't want to get really close to the tributes because in order for her to win she has to kill every single one of the tributes and if she has any connections with them it would be harder for her to kill her and easier for them to kill her.