The Democrats still have their slavery today, in the form of public housing, food stamps and illegal immigration. They haven't changed a bit. But the South has moved on while much of the North has apparently embraced slavery in its current form.
It was already in place. Lincoln offered to support the Corwin amendment which would have kept it even more firmly in place.
So since Lincoln was saying "If you like your slavery you can keep your slavery.", then how could the fight be over slavery?
Seems to me that the fight had to be over something else, because Lincoln offered protection for slavery before the war even started.