A person, thing, or source of information is considered "trustworthy" when it can reasonably be relied upon to perform as expected and/or promised. Trustworthiness generally stems from consistently positive performance of the person, thing, or source of information in question.
People sometimes trust things that are not trustworthy. For example, in the case of confirmation bias, people refer only to those sources they trust, and they tend to trust only sources that confirm their beliefs. This well-documented bias  sadly prevents many otherwise intelligent people from gathering information from new, different sources, which imprisons them inside a paradigm that is often imposed by the culture they grew in.
Because of the danger of trusting the untrustworthy, as Ronald Reagan often said, it is important to "Trust, but verify." This applies especially in the case of one's paradigm.