Explain why katniss has difficulty trusting people.

The reason that Katniss struggles with trust is because she sees it as a weakness. She even admits it to readers in Chapter 9.

The Games begin in two days, and trust will only be a weakness.

That makes sense in regards to the actual Hunger Games. 24 tributes go into the arena, and 1 comes out alive. Trusting someone eventually means being betrayed by that person. Katniss is realistic about her chances, and she knows that nobody has her best interests in mind except her. She trusts herself, but she sees no reason to trust anybody else.
A lot of this attitude of hers about trust is a direct result of growing up in District 12. It is the poorest and least populated of all of the districts. Food is an issue, and this has forced a lot of people to have an attitude of selfishness and distrust of each other. There are nice people that live in District 12, but even acts of altruism are met with suspicion. This attitude is actually encouraged by the Capitol. The Capitol knows that people that distrust each other and other districts are powerless to band together against the Capitol. Katniss's trust issues have been bred and brainwashed into her.

A way to plant hatred between the starving workers of the Seam and those who can generally count on supper and 15 thereby ensure we will never trust one another. “It’s to the Capitol’s advantage to have us divided among ourselves,” he might say if there were no ears to hear but mine.