Yours is an almost reasonable argument. You bring up a couple of valid points. If coercion was used at the secession conventions, then it may have thereby thwarted the actual will of the people.
The CSA did blunder and waste a legitimate opportunity for secession. They made several blunders in their efforts to break away.
But where I fault your argument is the thinking that they have to have good reasons or even coherent reasons for leaving. I believe people have a right...
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.
Without a well thought out rationale they have no hopes for international legitimacy short of defeating the other side handily on a battlefield, and the opposing side has all the ammunition to expose it as being a farce perpetuated by nutcases.
The DoI of 1776 was a beautiful document that laid out clear reasons (some more legit than others) for the break with the U.K., and wasn’t done as the first order of business unlike with the south in 1860 before Abe was even sworn in. It was the absolute last thing many of the founders wanted and only done so when they pretty much found out that George III was going to have them all killed. The secessionists wanted to “institute new Government” without actually stipulating what was wrong with the existing, and didnt even care to try to iron out misunderstandings.