"It was a war where one side had slave states and the other side was the confederacy" implies the following:

[only] "one side had slaves states"

"one side had slaves states" [and the other didn't].

[there was the side with slave states] "and the other side was the confederacy"

All of these are wrong but all are implied by the most common, good-faith parse of that sentence. Indeed using a strict parse of that sentence and De Morgan's theorem for inference it is outright wrong.

(Not buying into the "the civil war was not about slavery" argument. It was: https://www.tyseidule.com/excerpt.html)