Erasmus was a scholar, and his criticisms of the church are couched in obscure scholarly writings.
One criticism was that he flirted with some of the ideas of Luther. But in fact Erasmus was interested in changing the church, not destroying it. And he refused to go along with Luther completely.
The church was probably more against E than E against the church. The church found some of his biblical interpretations to support the heresy of Arianism. And they criticized him for not coming out strong enough against Luther.