I assume that you are asking about the Catholic Church and the sexual abuse scandals of recent times. If so, there are at least two reasons why the Church would cover up.
The first reason is organizational/bureaucratic. Scholars have found that people in organizations tend to lose sight of their responsiblities to those outside their organizations. Instead, they tend to act to preserve the organization even when it is in the wrong. Therefore, the Church might cover up the deeds of clergy (people within the organization) even though those deeds had hurt the children and their families (people outside the organization).
The second reasons is more specific to the Church. The Church would not want to publicize the fact that members of its clergy had been abusing children. This would undermine the entire existence of the Church because it would cause people to have less respect for and trust in the Church.