Of course, and that is my point---the argument is that the assumed right of secession based on a particular interpretation of the 10th amendment supposedly negates the very specific restrictions in the Constitution.
The problem with this argument is that it is completely based on an assumption. It tries to use the 10th amendment as a "get out of jail card," [pun partially intended ;) ]so to speak.
The assumption that the 10th amendment allows for unilaterial, unquestionable secession (which also means a complete negation of the entire Constitution) is, arguably, a great stretch.
Now, I have never argued that secession was absolutely illegal or impossible. In fact, I do believe it was probably something that could be carried out---but carefully. That said, I believe that unilateral secession by a state was against the spirit of the Constitution, if not the letter. In short, I have more of a problem with HOW the southern states tried to carry out secession rather than the fact that they did try.