That is what they did -- the People called secession conventions, seceded, and left the Union.
State equals People does not equal "state government".
There is no amalgamated "uber-People" that acts, or has ever acted, in a "mega-convention" of All the People of All the United States. That ain't the way we do business. That is because the lumpen People is a fiction, something invented by Hamilton to give the populous, big, commerce-dominated States (and the businessmen who dominated them) an edge over the rest of the People of every State. Hamilton's attempted coup was rejected by the People, who modified his plan in convention and with the Bill of Rights, to draw the teeth of the corporofascist federal tiger that Hamilton meant to unleash on them.
You Northern triumphalists are just celebrating your unjust Civil War victory over the Southern States and denying, as false propaganda, that the States exist any longer except as departments and lackeys of the federal government -- which you own.
Your position is precisely analogous to Slobodan Milosevich's, and like him, you will eventually see your faction-leaders on trial for usurpation and lese majeste' against the People, i.e. the States, for insulting their paramountcy, their sovereignty, and their rights and powers.
Ofcourse, like Stephens, Lee did not know as much as you brilliant Neo-Confederates.