The North didn't care about slavery, until they almost lost their ability to profit from it.
You could make the same scenario if the issue was gambling.
Once upon a time, America made money by gambling.
The South got really good at gambling, while the North didn't.
The North said "Come on, fellas. We're trying to make money, but we can't. We're going to try to sell hamburgers, instead. But we need a little financial boost to get started. Can you help us?"
The South said "Okay", and continued to contribute gambling money to the North's hamburger business.
But the North still couldn't make a profit. So the North demanded more money from the South.
The South protested, but kept contributing. They felt that some day, the North would pass the tipping point, and finally profit and support themselves.
Eventually, the North was taking half of the South's gambling profits, and the South said "Enough! We're leaving."
That's when the North decided to go to war with the South. The North invaded.
They began to trash talk the concept of gambling, all the while raiding the casinos and stealing the South's money.
Trash talk included "You beat your black jack dealers! You hate the black jack dealers, don't you?"
The North even drew pictures of casino owners beating up black jack dealers on their hamburger wrappers. (It kinda looked like the political cartoon you posted.)
All the South wanted to do was walk away, and continue to be self-sufficient.