Why were people in the north so upset over seven slave states leaving the Union? Why was peaceful separation so enraging.
I'm going to couple these two because they are conjoined anyway. It is my opinion that much of the reaction of the north wasn't due to the act of secession but of the tactics of secession. It was anything but peaceful. The rebels initiated their "peaceful secession" by raiding (at gunpoint) federal treasuries and mints, armories, and stock houses in a frenzy of theft. The rebels didn't negotiate their way out of the union - they chose to fight their way out.
It (secession) would seem like a good solution to the issue.
Possibly, but not probably. For 400 years the new continent had been subjected to constant struggles for acquisition and dominance. There is no reason to believe that those struggles would not continue - or increase now that one half of the nation had taken up an adversarial position to the other half. Lincoln, like his predecessor Buchanan, believed that he did not have constitutional authority to interfere with secession. He favored negotiation in the hope that cooler heads would prevail and the secessionists would abandon their foolhardy plan. The south's actions at Sumter ended any hope of that.
The likelihood is that what we knew as The United States would cease to exist with nations like Great Britain devouring us - starting with the confederacy. "We must hang together or we will certainly hang separately"
Claiming that no state or group of states can ever leave the union sounds more like the former Soviet Union than the union of free and independent states that formed the constitutional union.
I don't know anyone other than lost causers who make that claim. I certainly do not believe it to be accurate. But secession as practiced by the would-be confederates was certainly illegal and dishonorable.