Article 2, Section 3.
he shall take care that the laws be faithfully executed
It's hard to imagine someone would post on this issue and be so ignorant of the record they wouldn't know that President Lincoln said in his first inaugural:
"I therefore consider that, in view of the Constitution and the laws, the Union is unbroken; and to the extent of my ability I shall take care, as the Constitution itself expressly enjoins upon me, that the laws of the Union be faithfully executed in all the States. Doing this I deem to be only a simple duty on my part; and I shall perform it so far as practicable, unless my rightful masters, the American people, shall withhold the requisite means, or in some authoritative manner direct the contrary. I trust this will not be regarded as a menace, but only as the declared purpose of the Union that it WILL Constitutionally defend and maintain itself."
And that is what happened.
Walt
But the point is, the Confederate States were not among "all the states". They had seceeded from the union and the Constitution no longer applied to them.
If you wish to argue that they had no right to seceed, you have to repudiate the Declaration of Independence. If the 13 Colonies had the right to seceed from England, then the southern states had the right to seceed from the US.