Obviously it depends on what you mean by "basic." "Fighting for home" is a pretty primal reason, but if you hoisted the Jolly Roger right now and went to war against the US for your "home" it wouldn't make much sense. You wouldn't have much of a reason for fighting. Politically and historically, slavery was a more "basic" reason for war than "home."
In other words, if you love your home but don't have any more fundamental reason for fighting there's no war. If you have something else to fight over, people will line up on this side or that on the basis of where their home is. It may be a reason why a particular person fights or sympathizes with this side or that, but no, it's not a "more basic" reason for the war.
And no, Robert E. Lee didn't "oppose" slavery, any more than he "opposed" intemperate drinking or bad language. Even that is too strong, as he accepted slavery in a way that he wouldn't put up with rudeness or coarseness. "Disapprove" is too strong too. Maybe, "regret" is the best word for Lee's feelings about slavery.
"Politically and historically, slavery was a more "basic" reason for war than "home."
And that is where analysis goes awry. Do you honestly suppose that my second great grandfather had anything on his mind, when he ran off and enlisted in the NC 21st, other than finding his older brothers? Do you think that, maybe, it just might have been more "primal," as you put it, rather than political? It certainly wasn't historical to him; it was contemporary reality.
Grotius' theory of Just War holds that self-defense against an invader is justification for the use of force.
"So far from engaging in a war to perpetuate slavery, I am rejoiced that slavery is abolished. I believe it will be greatly for the interests of the South. So fully am I satisfied of this, as regards Virginia especially, that I would cheerfully have lost all I have lost by the war, and have suffered all I have suffered, to have this object attained."
Douglas S. Freeman, Robert E. Lee, New York, NY: Charles Scribner's Sons (1934), Vol IV, p. 401
Lee was fundamentally opposed to slavery and secession, but he loved Virginia more.
So was Stonewall Jackson. I believe the biggest problem was that even though many in the South disagreed with the institution, they also believed that it was an example of States-Rights, and that the North was going to use it as an excuse to destroy the South.