This is like saying there are two ways to leave the English Union. By petitioning Parliament or by asserting your Independence.
The US chose the later. They chose exactly correctly. The Southerners chose the same path.
That’s like Michael Scott (from TV’s “The Office”) walking into the middle of the room and shouting, “I...Declare....BANKRUPTCY!”
There’s more to it than the Colonists declaring independence. They knew that they were declaring a open, armed rebellion against the authority of the crown. They knew the likely consequences if they were to fail.
None of that existed in 1860. The southern states weren’t without representation. No armies were marching into their towns and seizing their citizens or their property. There was no moral or legal justification for quitting the union. Being angry isn’t justification.