Why didn't the North let the South secede?

[Democracyinkind]

14. Fort Sumter?

The practical reason - Fort Sumter.

Lincoln's deeper reasonings are best illustrated in his Message to Congress in Special Session on July 4th, 1861.
I'll quote the part that covers Lincolns political reasoning as an example. Try to read the whole thing though - I've never met anyone who wasn't utterly convinced by it.

&quot ...)And this issue embraces more than the fate of these United States. It presents to the whole family of man the question, whether a constitutional republic, or a 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 discontented individuals, too few in numbers to control 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 their 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?’(...)’"

http://teachingamericanhistory.org/library/index.asp?document=1063