So, this annoys me to no end, because the first dude is technically right, Lincoln came in to office with no intention to outlaw slavery, although he did want to keep it confined to the states it was already legal in. And what he’s actually wrong about is that Lincoln made it about slavery to get the support of the northerners - he actually made sure that it northerners believed it was about “keeping the union together.” Remember the union still had the slave states of Kentucky, West Virginia, Maryland, Delaware and Missouri. He wanted to keep these states in the union.
Lincoln (through Seward) stressed the anti-slavery stuff to Europeans, many of whom wanted to intervene on the side of the confederacy because that was where they got their cotton. The industrial north also was a threat to industrial Europe, but the agrarian south was a source of raw materials. But by stressing the anti-slavery stuff in Europe (and then of course the emancipation proclamation which didn’t actually outlaw slavery in the border states) he ensured Europe could not intervene on behalf of the confederacy since it would be so unpopular. So, in the states it was about the union, abroad it was about slavery.
But anyway, he’s right on a technicality that, for Lincoln, it was not really about slavery. But this does not mean the war itself was not about slavery. His conclusion rests on the assumption that in a war, two sides must be diametrically opposed to one another, so if Lincoln and the north were not fighting against slavery, therefore the south could not be fighting for slavery.
But as others have pointed out, the south explicitly says they are fighting to preserve the institution of slavery. They are worried about waning political power also - if Lincoln stopped the spread of slavery across the continent as he desired, the growth of free states would mean congress would not be as evenly split between slave and free states, opening up the possibility of legislating an end to slavery.
So the war was about slavery, and would not have occurred without slavery. Often we point to the Battle of Sumter as the beginning of the civil war, but many historians also point out the popular civil war could instead be said to begin in 1859 in Harper’s Ferry, or with Bleeding Kansas and the Pottawotamie Massacre, or maybe the caning of Charles sumner or the murder of Elijah Lovejoy, or any of the political battles that arose when the US began to expand west and the question arose “what about slavery.” All of these events are directly about slavery and it would be difficult to argue otherwise.
And also, just as a last thing “many southern generals didn’t care about slavery.” I have no idea how true that is and it doesn’t matter, because the war was not fought because of southern generals but because of politicians, southern landowners, and an economy resting on the subjugation of Black people, and that’s why they were fighting.