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.
In Marbury v Madison, Chief Justice Marshall disagreed:
It is also not entirely unworthy of observation, that in declaring what shall be the supreme law of the land, the constitution itself is first mentioned; and not the laws of the United States generally, but those only which shall be made in pursuance of the constitution, have that rank.
Federal laws (if any) must be made pursuant to the Constitution. It is the legislature that passes legislation, not the judiciary or executive branches. Marshall noted that the legislature just can't make laws up because they want to:
The powers of the legislature are defined and limited, and that those limits may not he mistaken, or forgotten, the constitution is written. To what purpose are powers limited, and to what purpose is that limitation committed to writing, if these limits may, at any time, be passed by those intended to be restrained? The distinction between a government with limited and unlimited powers is abolished, if those limits do not confine the persons on whom they are imposed, and if acts prohibited and acts allowed, are of equal obligation. It is a proposition too plain to be contested, that the constitution controls any legislative act repugnant to it; or, that the legislature may alter the constitution by an ordinary act.
Nowhere is secession a right reserved to the states (not even the 10th amendment).
Marshall also opined that it "cannot be presumed that any clause in the constitution is intended to be without effect; and, therefore, such a construction is inadmissible unless the words require it." Your claim that the right of secession is not reserved is contrary to the construction of the 10th Amendment, which states that the "powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." There must be a grant of power to the federal government to prohibit secession, or a prohibition upon the states from seceding.
Of course, some will claim that the people have the right to prevent secession. First and foremost, the ratifications were acts of the people of separate states, not the acts of all the people as a common mass. In US Term Limits v Thornton, Justice Thomas wrote:
The ultimate source of the Constitution's authority is the consent of the people of each individual State, not the consent of the undifferentiated people of the Nation as a whole. The ratification procedure erected by Article VII makes this point clear. The Constitution took effect once it had been ratified by the people gathered in convention in nine different States. But the Constitution went into effect only "between the States so ratifying the same," Art. VII; it did not bind the people of North Carolina until they had accepted it.
... As far as the Federal Constitution is concerned, then, the States can exercise all powers that the Constitution does not withhold from them. The Federal Government and the States thus face different default rules: where the Constitution is silent about the exercise of a particular power--that is, where the Constitution does not speak either expressly or by necessary implication--the Federal Government lacks that power and the States enjoy it.
... To be sure, when the Tenth Amendment uses the phrase "the people," it does not specify whether it is referring to the people of each State or the people of the Nation as a whole. But the latter interpretation would make the Amendment pointless: there would have been no reason to provide that where the Constitution is silent about whether a particular power resides at the state level, it might or might not do so. In addition, it would make no sense to speak of powers as being reserved to the undifferentiated people of the Nation as a whole, because the Constitution does not contemplate that those people will either exercise power or delegate it. The Constitution simply does not recognize any mechanism for action by the undifferentiated people of the Nation.
... In short, the notion of popular sovereignty that undergirds the Constitution does not erase state boundaries, but rather tracks them. The people of each State obviously did trust their fate to the people of the several States when they consented to the Constitution; not only did they empower the governmental institutions of the United States, but they also agreed to be bound by constitutional amendments that they themselves refused to ratify. See Art. V (providing that proposed amendments shall take effect upon ratification by three quarters of the States). At the same time, however, the people of each State retained their separate political identities. As Chief Justice Marshall put it, "[n]o political dreamer was ever wild enough to think of breaking down the lines which separate the States, and of compounding the American people into one common mass." McCulloch v. Maryland, 4 Wheat. 316, 403 (1819).