Where did you get that idea? Nothing in the Constitution suggest that.
It was decided rather emphatically 1861-1865.
Article I Section 10 of the US Constitution prohibits states from negotiating trade agreements, declaring war, or conducting diplomacy because these are powers granted to the Federal Government. That makes it pretty clear that states are not sovereign nations. If they cannot negotiate their own treaties or trade deals, they certainly don't have the power to leave the union at will. If such a right existed in the US Constitution, there would never have been a US Civil War.