Why weaken it when your purposes can become one?
I take it you're addressing why the protagonist might distrust the Chantry of Andraste, and therefore why the main character might want to diminish the power of the Chantry, or make it an impotent organization altogether. In terms of the elven protagonist, the Dalish being forced to live nomadic lifestyles because their religion and culture are outlawed could be one of many reasons, while an mage protagonist who believes in autonomy for the Circles might take an issue with how mages are imprisoned in Circles as a primary reason to oppose working with the Chantry, or even share the view that the Chantry controlled Circles are an institution that's tantamount to slavery. It all boils down to the simple fact that there are reasons why some might not be inclined to trust the Chantry, or want an alliance with the organization.
I don't see my Dalish mage trusting the Chantry of Andraste given everything that's transpired between the Chantry and the Dalish, and I can imagine there are others who might play as characters who don't want to put themselves in a position where they could be stabbed in the back by an organization they have no reason to have any faith in.