States are admitted to the Union only with the consent of the other states through a vote in Congress. Once they have been allowed to join, they cannot split into two or more states, combine with any other state, even change their border by a fraction of an inch without the approval of the other states through a vote in Congress. It is no great stretch to come to the conclusion that they should require the consent of the other states to leave entirely as well. The interest of the other states are entitled to protection.
The Confederate states were not trying to overthrow, supplant or replace the existing US federal government...only to withdraw from it and establish a new federal government.
The southern states walked away from the Union and all the obligations built up by the nation as a whole while they were part of it. They abrogated responsibility for their share of the national debt, took whatever federal property they wished without compensation, and blocked remaining states from access to the sea. How can their actions be considered fair treatment towards the remaining states? Why aren't the interests of the rest of the U.S. of any consideration in this? Why do only the seceding states count?
Its funny you mention that...are you aware of the background of the creation of the state of West Virginia? Now, that was almost unquestionably an illegal, unconstitutional act orchestrated by pro-Union forces to punish the state of Virginia.