Lincoln is talking about the right of revolution in that quote. Not the made up legal “secession” the southern rebels claimed was hidden in the constitution.
Notice it says “having the power”. Not any people anywhere can just claim independence from their existing government and that existing government has to let them go.
And yes secession was treason. The Supreme Court already had declared in three Supreme Court Cases that the constitution was ratified by the people m, not the states, and could only be undone by all the people, no subset of the people. The earliest decisions by the Supreme Court proclaiming this was in Chisholm vs Georgia 1793, just five years after the ratification of the constitution. It said this;
“It is remarkable that, in establishing it, the people exercised their own rights, and their own proper sovereignty, and, conscious of the plenitude of it, they declared with becoming dignity, “We the people of the United States, do ordain and establish this Constitution.” Here we see the people acting as sovereigns of the whole country, and, in the language of sovereignty, establishing a Constitution by which it was their will that the State governments should be bound, and to which the State Constitutions should be made to conform.”
In other words the people, as a whole, made the constitution and bound the states to it.
Also a President, when faced with the threat of secession, had already set the precedent thirty years earlier in his nullification proclamation.
“This, then, is the position in which we stand. A small majority of the citizens of one State in the Union have elected delegates to a State convention; that convention has ordained that all the revenue laws of the United States must be repealed, or that they are no longer a member of the Union. The governor of that State has recommended to the legislature the raising of an army to carry the secession into effect, and that he may be empowered to give clearances to vessels in the name of the State. No act of violent opposition to the laws has yet been committed, but such a state of things is hourly apprehended, and it is the intent of this instrument to PROCLAIM, not only that the duty imposed on me by the Constitution, ‘` to take care that the laws be faithfully executed,” shall be performed to the extent of the powers already vested in me by law or of such others as the wisdom of Congress shall devise and Entrust to me for that purpose; but to warn the citizens of South Carolina, who have been deluded into an opposition to the laws, of the danger they will incur by obedience to the illegal and disorganizing ordinance of the convention-to exhort those who have refused to support it to persevere in their determination to uphold the Constitution and laws of their country, and to point out to all the perilous situation into which the good people of that State have been led, and that the course they are urged to pursue is one of ruin and disgrace to the very State whose rights they affect to support.”
“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.“
Andrew Jackson 1832
This is the precedent that both Buchanan and Lincoln followed when dealing with the “secessionist” in 1860-1865.
The southern rebels should have been under no delusion that “secession” was legal or allowed.
Thomas Jefferson believed states had a right to secede. He was correct. That is why Jefferson Davis was not tried for treason. He could have been tried but wasn’t. The Federal Government knew they would have lost the case of they brought it.