I'll leave the specifics to those on the Forum with more legal and/or political knowledge than myself...but here are some of the "bottom lines" as I've read these arguments in the past.
1) Secession arguments are about like the arguments people have about paying Federal Taxes. Whether or not the Constitution says its legal or not...neither can, nor will be allowed, to happen.(And if you've read the anti-tax arguments; they are constitutionally compelling...until the judge sentences the person to jail time and fines).
2) Like if or not, the States are not as "independent" from the Federal Government as some would like to believe; the States are too "intertwined" with the Federal Government on so many levels to argue legitimate "independence".
3) There is a huge difference between being "pissed off" at the Feds; whether it be for taxation, wasteful spending or imposition of certain laws...and that Government truly...and I mean truly taking away ones fundamental rights of self-determination, "life, liberty and the pursuit of happiness".
There is no question that people everyday have these rights trampled on in some way or form (and not exclusively by the Feds; but also by State, and yes, local governments.)...but it would be difficult to prove that on a State Wide Basis, thus "justifying" secession.
In other words, that the Feds have in fact singled out a particular State and its citizens; and then has systematically denied those citizens their basic and fundamental rights.
4) Now...this is where the arguments get REALLY heated...and that is whether of not the Civil War "settled" the argument of a States right to secede...and that one I'll have to leave for the more knowlegable ones on this site.
Again...these are what tend to be the most common "bottom-line" arguments when these threads come up, in what ultimately tends to be a very interesting topic for discussion.