Specifically regarding people not trusting law enforcement, that's because in the U.S. police don't have a responsibility to protect individuals, just the community as a whole (see https://en.wikipedia.org/wiki/Warren_v._District_of_Columbia). In addition, police often can't get to the scene of a crime in progress soon enough to prevent harm to the victims. As long as criminals are armed and able to commit crimes before the police can stop them, it seems reasonable that some citizens would choose to own guns in an attempt to protect themselves or their families.