If the North was not trying to end slavery why would the south need to secede to preserve it?
Lincoln indeed was an abolitionist, and had spoken in the strongest terms against slavery. The South was logically afraid his presidency would push for it, even though he had not promised he would, and on more than one occasion even promised to keep slavery for the sake of the union. Therefore thinking Lincoln MIGHT push for abolition, the powers that be in the South seceded, seeding their own nightmare.
Lincoln and the North initially went to war for UNION not abolition, even though they ended the war with the abolition of slavery. The Emancipation Proclamation of 1863 fundamentally changed the purpose of the war--from the North's perspective.