In matters of state powers vs state obligations and of prohibitions on states, the only applicable law is the Constitution. Since there is no prohibition against secession anywhere in any article or any amendment, then secession is a reserved state power, and a right reserved to the people of the states. The powers of the states and the rights of the people do not have to be listed to exist. the powers of the federal government do have to be listed. Those are the points of the ninth and tenth amendments.
The US Constitution is a very short, concise document written in plain, spare language. What is in the text is the supreme law of the land. What may or may not be implied is in the imaginations of men other than those who crafted the document and quite simply has no force of law.
A Constitutional argument which avoids citing the text of the document is no argument at all, it's a waste of time for all involved. You haven't addressed the legality of secession at all, other than to claim that it's illegal because you say so. Necessity aside, any power not delegated to the United States nor prohibited to the states by the Constitution is indeed a reserved power of the states and/or a reserved right of the people.
Try again and stick to what appears in the text. Your own inductive leaps of logic weren't ratified by the states and aren't part of the supreme law of the land.
Gee. I wonder why James Madison didn't see that? Maybe he was just another 'damnyankee'.