Because she knows that if they try to climb up the tree to kill her, the branch would snap because they are too heavy
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When they planned to blow up the food supplies, the advantage they had was that Rue and Katniss were from very poor districts where as the Career tributes have never missed a meal or been hungry before in their life. And if the food supply is suddenly eliminated, it makes the Games end a little bit faster.
Katniss finds Peeta near a stream, camouflaged in the ground.
Johanna cuts Katniss' arm open and takes the tracker out of her arm in the quell and Chaff gave Katniss a kiss on the lips after the tributes parade.
remember who the enemy is. (the capitol, not the other tributes) and not to make the game makers mad.....
Think about it. Over the next month, she will have killed or watched many of these tributes die. Eventually, some of these tributes will try to kill her. Katniss doesn't want to kill anyone, and as she said in District 12, she doesn't handle injured or dead people very well (even though her mother's a healer).