I've had a certain amount of success in teaching gatherings of Lutherans about the problem of CCM by initially stating that it is "about how God comes to us." Does he come by virtue of his own power, his own Word (Christ), directly to us, or must God be channeled to us through a clerical system which is endowed with a special power to make God / Jesus present.
Obviously, Lutherans believe that all power is in the Word, because of Christ's explicit promises to us (example: "This is my body...") as recorded for us in Scripture.
You can tell folks that Lutheranism was a revolution in thinking 500 years ago, and now! It is not merely a spirituality, as is now fashionable to say among our ecumenical leaders. Lutheranism is itself a modern view; it cracked the clerical / sacramental system of the Roman-Orthodox-Episcopal Churches, and it still threatens their clerical systems today. Yes, it does.
For Lutherans, CCM takes on the pre-Reformation view of clergy; it elevates clergy; it states their necessity; and it diminishes the pre-eminence of the power of the Word alone -- of Jesus Christ alone.
See Section 5 of CCM, where a sneaky little paragraph declares bishops to be necessary for the unity and apostolicity of the church. As Lutherans, we say unity comes from Christ alone, and not through, or because of, clergy. I loath this Section of CCM; it occurs to me as absolute idolatry.
See Section 8 of CCM, where it is declared: "(W)e agree that the one ordained ministry will be shared between the two churches in a common pattern for the sake of common mission." Key phrase: "...one ordained ministry will be shared...."
See Section 14 of CCM, where it is declared: "The creation of a common and fully interchangeable ministry of bishops in full communion will occur with the incorporation of all active bishops in the historic episcopal succession...." Key phrase: "...common and fully interchangeable...."
What will a fully interchangeable ministry of bishops in full communion look like? CCM is quite clear on this; and, it won't be Lutheran:
Section 16 of CCM states that the Anglican Ordinals (rules on ordination) of 1662 will be imposed on the shared ministry: "The purpose of temporarily suspending this restriction (meaning, the ordinals) ...is precisely in order to secure the future implementation of the ordinals' same principle in the sharing of ordained ministries...."
Quote these passages from the text of CCM.
CCM is about clergy, their roles and their purpose. CCM is decidedly and explicitly non-Lutheran. The text of CCM is clear in this matter; it is not ambiguous, it merely uses language that is unfamiliar to most Lutherans.
When lay people put these key portions of the text together, they will understand the problem with CCM. But, they must first know how God comes to us...a review of Luther's explanation to the 3rd Article of the Apostles Creed is a good starting point: "...but the Holy Spirit has called me through the Gospel, enlightened me with his gifts, and sanctified and kept me in true faith."
It's God who has called us...he comes to us directly...not through the intermediary of a member of the clergy.