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While he is a superstar of this particular subreddit, I will actually link to a response written by u/Georgy_K_Zhukov in r/badhistory.
In short, the trick is to be able to understand that the war resulted because of the South's concerns about slavery and their desire to secede while acknowledging that it was not a war of abolition until the war was nearly halfway done.
The war was TECHNICALLY over a state's ability to secede from the union (that is, actually, the "state's right" in question, though most people don't realize it). However, without the drive to protect slavery, the southern states would never have seceded.
Those who claim the war was only about states' rights and not really that much about slavery are very much wrong. Equally as wrong are those who claim the war was a war of abolition (at least, before January 1st, 1863, at which point it did become a war of abolition). The South fought to secede for the EXPLICIT purpose of protecting slavery (I believe the extensive citations in the linked response are sufficient). The Union states fought (initially) to deny the ability to secede alone, with no intent to end slavery.