The Civil War WAS about slavery - that's what the people who started the Civil War, the leaders of the so-called "Confederacy" said themselves. You can read their own statements and documents - they explicitly said the SOLE reason for their secession was slavery, and they denied that there was any other reason. Arguments that the Civil War was not about slavery are post-war propaganda - lies made up to justify their rebellion after the fact.
The common soldier in the rebel army had virtually no political say - they were fighting because they were forced to, or because they were lied to, but they absolutely, 100% were fighting for SLAVERY, because that's why their leaders started that war. Every single soldier in gray was fighting for slavery, whether he wanted to or not.
The North was not trying to force any laws on the South - in fact, it was the other way around! Read about the 1850 Fugitive Slave Act, maybe the most disgusting law ever enacted in the history of the United States. It was enacted to try and prevent a civil war from breaking out in 1850, as a result of the stress the war with Mexico and conquest of huge new territories had caused between the pro-slavery forces who supported the war, and the free soilers who didn't want slavery to expand into California and Arizona and Nevada. The law forced state officials to help hunt down and return runaway slaves, and there was no way for a person accused of being a runaway slave to defend themselves - a runaway slave hunter could just point to a black man and say "this is the runaway slave," and LEGALLY force that man into slavery, even if he had been born free in a free state. Needless to say, many Northern states refused to fully enforce that law, and demanded its repeal - and these demands were one of the chief reasons the secessionist leaders used to justify their rebellion!
They wanted to impose slavery on the whole country! They wanted free states to be forced to hunt down their runaway slaves. They wanted free states to silence those who spoke out against slavery (freedom of speech be damned). They wanted to be able to bring their slaves into free states, both temporarily and permanently (making the concept of a free state meaningless). They wanted to expand slavery into ALL the territories. They wanted to conquer Cuba and Hispaniola, to further expand slavery. They weren't angry at Northern states for "imposing" laws on them - they were angry that Northern states were resisting having pro-slavery laws forced on them!
Lincoln wrote that sentence to Horace Greeley several weeks after he had already decided to issue the Emancipation Proclamation (which was a death blow to slavery, regardless of what it did by its own words - slavery could never survive after the EP because it would render slavery legal in so few places that it would be strangled by geography and politics, allowing slavery to be destroyed relatively quickly and without a massive political fight) - in other words, when Lincoln wrote those words, he was LYING to Greeley. Lincoln was spinning, what a politician does best - denying his anti-slavery measures to avoid scaring away those who didn't care about slavery while he built up the support to destroy slavery. It was actually quite brilliant, politically, and Lincoln, just before he was assassinated, was calling for political rights for the freed slaves - the right to vote prominent among them. It turns out that your opinion can change over time.
So, the Civil War ended, and you know what happened? When black Americans started to demand civil rights in the 1950's, those Confederate flags started showing up, held by white Americans who were torturing and murdering those civil rights marchers. Those flags were used as a symbol of white supremacy, of opposition to the concept of equality under the law. Those flags have never stood for anything else.