Please cite the relevent powers from the Constitution which were delegated or prohibited which would invalidate secession.
(*sigh*) How many times do I have to repeat myself? Secession per se is not unconstitutional. However, Article IV, Section III makes it clear the Congressional approval is needed for change in the status of a state. And Article I, Section 10 makes it clear that unilateral action when such actions impact the interests of other states are forbidden. So it is the unilateral aspect of the southern action which made it illegal.