I'm only a high school student, but I did take APUSH. I know that doesn't give me much merit, but I can point you in the right direction.
It all depends on who you ask. When looking at the Constitution (or other legal documents) you have a strict and loose . For a strict interpretation, you can only do what the Constitution tells you you can do. For a loose interpretation, you can do anything the up to the point Constitution tells you you can't do it.
For example: You ask mom if you can go to the movies with Billy. She says yes.
Under a strict interpretation, you would go watch a movie and come back. Under a loose interpretation, you buy a bunch of candy at the the theater, watch 4 movies, and come back at midnight because she never said you couldn't do that.
Although there is no mention of secession in the Constitution, the Declaration of Independence says
"That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn that mankind are more disposed to suffer, while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security."
So you could take that to mean that the government was destructive to the South, so they made their own government. Or you could say that the South has absolutely no merit to leave the Union.
If I confused something, could a real historian please correct me because as much as I do love this stuff it gets really confusing.