A think a longer (but more clarifying) statement would be "slavery was the primary motivational reason for the War for the Confederates." Saying "the reason for the war" is already misleading because it assumes there was a reason than applied to both sides. On the contrary, the Union didn't conquer the South out of the goodness of their hearts because they were (mostly) fervent abolitionists. I think that's the misleading thing your summary implies.