While I believe the secession justifications of southern and border states are morally reprehensible, I do not understand what made the act itself necessarily illegal, or why unionists feared disunion so much. Why did Lincoln chose war over simply letting the states go, or even only embargoing their commerce and trade?
There was a very thorough answer to this by u/secessionisillegal over here. (Which could have been expected, given the name!). There was a more concise one by u/freedmanspatrol over here
As to why the Union couldn't let them go, there was the question of all the Federal property in the South, that the South just felt entitled to take- like Ft Sumter. There was the problem of the new territories in the West- the South had an agricultural economy and needed new land in order to grow it, and clearly felt entitled to some of that land. And Lincoln very much feared secession leading to more secession, more anarchy:
The distinct issue, "Immediate dissolution or blood"...embraces more than the fate of these United States. It presents to the whole family of man the question of whether a constitutional republic or democracy -- a government of the people, by the same people -- can or cannot maintain its territorial integrity against its own domestic foes. It presents the question whether the discontented individuals -- too few in numbers to control the administration, according to organic law, in any case -- can always, upon the pretenses made in this case or on any other pretenses, or arbitrarily without any pretense, break up the government and thus practically put an end to free government upon the earth. It forces us to ask: "Is there, in all republics, this inherent and fatal weakness? Must a government, of necessity, be too strong for the liberties of its own people, or too weak to maintain its own existence?"