When one has been abandoned
When one has been abused
When one has been cheated on by a boyfriend or girlfriend
When a friend or sibling betrays one's trust (by spreading a rumor, rejecting one as a friend, telling one's secret, etc.)
When one has been disillusioned through the fall of a mentor, role model, or trusted organization
When one has been used as a pawn (by a friend trying to gain popularity, a political group using one to further their agenda, etc.)
When one's parent was taken advantage of (being laid off after a long stretch of loyal employment, being scammed out of their life savings, etc.)
When those in authority who are supposed to protect turn out to be incompetent or corrupt (the police force, the church, the government, etc.)

There are five basic human needs that, when missing from a character's life, could motivate them to pursue this goal. The following needs are all possibilities, but only one of them should be the primary driver for any given character. For more information on the relationship between human needs and outer motivations, please see this Character Motivation tutorial.

Love and Belonging: An inability to trust will always impact the character's relationships, making it difficult for them to connect with others. As a result, that lack of meaningful relationships with others is going to be a driving force behind learning to trust others and regain what has been lost.
Safety and Security: In certain situations, a character's inability to trust others will undermine their safety and security. Their skepticism toward the police force, for instance, will keep them from reaching out when help is needed. If their living situation becomes so bad that the police are the only ones who can promise safety and security, the character may choose to pursue this motivation.