How does the complexity of the world around us affect the reliability of our opinions? Motivated by this question, we discuss a simple model where an observer gradually forms opinions about a world composed of subjects interconnected by a signed network of mutual trust and distrust. We show that this opinion formation process is highly fragile. As a result, an individual who initially trusts a few credible information sources, for example, may end up trusting the deceptive ones even if only a small number of trust relations exist between the credible and deceptive sources. The presented framework allows us to ask further questions such as how to improve the reliability of the formed opinions and why there is a phase transition in opinion formation.