The CLC was created primarily (though not solely) from congregations that broke away from the Wisconsin Evangelical Lutheran Synod (WELS) and the Evangelical Lutheran Synod (ELS) in a disagreement about the application of the principles of Christian fellowship (in this context, an agreement of a unity of belief). The CLC maintained that the WELS and ELS misapplied those principles by not breaking with the Synodical Conference and the Lutheran Church–Missouri Synod after they had publicly recognized doctrinal error within those bodies.