“There was no right for a state to leave the Union unilaterally.”
Show me where in the US Constitution, as it existed in 1860 and 1861, where states were precluded from seceding.
There is nothing there to prevent it, so there is no reason why a state may not be permitted to leave. The question is in the manner in which they leave. Since states are only admitted to begin with when a majority of the existing states approve as indicated by a vote in both houses of Congress, and since they are permitted to split or combine or change their border by a fraction of an inch only with the approval of the existing states as expressed through a vote in both houses of Congress, and since they are forbidden to take certain actions which may impact the interests of other states without approval of Congress, then it's no great stretch to come to the conclusion that leaving should require the same thing. States may leave with the consent of the other states as expressed through a vote in both houses of Congress. States remaining have rights that need to be protected, as do the states leaving. You keep ignoring that. The only way to make sure the separation is peaceful and equitable is to negotiate issues of disagreement, vote on the proposal, and wave the departing states bye,bye.