Theological denominationalism ultimately denies reality to any apparent doctrinal differences among the "denominations", reducing all differences to mere matters de nomina--"of names".
A denomination in this sense is created when part of a church no longer feel they can accept the leadership of that church as a spiritual leadership due to a different view of doctrine or what they see as immoral behaviour, but the schism does not in any way reflect either group leaving the Church as a theoretical whole.
This doctrine is, of course, unacceptable to those Christian groups that see themselves as being the "One Holy Catholic and Apostolic Church" as a whole. This includes the Eastern Orthodox, the Roman Catholics, and the Oriental Orthodox Communion, each of which claims to be the exclusive "Holy, Catholic, and Apostolic Church". In these "denominations", it is not possible to have a "purely administrative" separation, and any such attempts automatically are a type of schism.