Lincoln chose the battlefield. The south chose the state legislatures.
As a pretext to choosing the battlefield. Again poor choices for the south to make.
When it reached the Supreme Court, in Texas v. White, it was ruled that the southern legislatures did not have authority to secede, that therefore they had not.
Of course the southern slave power knew that there was no state legislature authority to secede with out cause. They knew their cause was wrong, but they thought they could win on the battlefield. That is why the hotheads fired on Ft Sumter. Because of that great wrong, put together with the other great wrongs of the southern slave power cause, some 40 regiments of southern men served in the Union army.