Most law enforcement officers do a good job. Most encounters between police and the public are completely safe. However, there are a few tragic times where police actions have been careless, resulting in the deaths of innocent people. By and large, though, the public can generally trust the police to do the right things.
Police are not fully trustworthy, simply because they are human beings. Human beings are not perfect, and never will be. Police officers have a very difficult and risky job, and they are bound to make mistakes simply because of their flaws as human beings and the high pressure of their jobs. Additionally, certain groups have even less reason to trust the police because of implicit biases, and occasionally conscious prejudices. For example, African-Americans have more reason to not trust the police, since they are more likely assumed to be guilty, mostly because of implicit bias.
It's no secret that police misconduct rates are higher than ever before. Police don't care about the little people. They go into their position in order to have power. They only work for 20 years and then retire with a huge pension. They shoot people if they don't like their race or for any other reason and they're never held accountable.
For the most part, the public and rely on and trust the police. There are those situations however, where this is not the case. Sometimes the police are lax in following the rules when determining if a person is breaking the law. They act rashly and don't get all the necessary information, and/or don't follow proper procedure.