Secession is not treason. Making war on them (the states) is. Lincoln is the only one who did that.
"The laws of the United States must be executed. I have no discretionary power on the subject-my duty is emphatically pronounced in the Constitution. Those who told you that you might peaceably prevent their execution, deceived you-they could not have been deceived themselves. They know that a forcible opposition could alone prevent the execution of the laws, and they know that such opposition must be repelled. Their object is disunion, hut be not deceived by names; disunion, by armed force, is TREASON."
Lincoln, on the other hand, was carrying out his constitutional duty to suppress insurrection. This duty is spelled out in the constitution and the means to do so was later delegated to the executive branch by congress in the militia acts of 1792 and 1795.