I think it’s not so much that the Church is horrible at self-reflection as the fact that Church teaching emphasizes personal guilt over institutional guilt. I don’t think the problem comes down to anything intrinsic to the Church, rather it is the result of individual sin, whether of sex abusers or of bishops who covered it up.
And it also depends on what you mean by “the Church.” Nearly every saint I’ve read writes in some way about how horrible their own sins are and how much evil there is in the Church.