The Constitution does in fact say that states cannot unilaterally secede from the Union, as it is Congress, not the states, that has the power to regulate and dispose of U.S. territory.
It says no such thing.
We've done this before, you know. I'm perfectly willing to do it again.
United States Constitution said:
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
This one's the kicker. When taken in the context of the Supremacy Clause, we see that the states cannot violate the territorial sovereignty of the United States. Secession is such a violation. Here is that Clause, in case you've forgotten:
United States Constitution said:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
The power to regulate and dispose of United States territory is explicitly vested in the Congress. Nothing in the Constitution may be interpreted to prejudice the territorial claims of the United States. No state law may contravene federal law or the Constitution. That's the 10th Amendment argument and the method of state ordinance of secession both out the window. There is one, and only one, constitutional method by which a state may leave the Union, and that is by the passage of a constitutional amendment.