The choice Lincoln put them to was to fire to drive an invader away, or not fire and be occupied without defending themselves. If somebody is invading your home and you fire a warning shot to drive him away, you are not the aggressor. He is. He's the one who was invading your home after all.
You are correct. A civil war....a true civil war is when one or more sides fight for control over the central government. That was no more the case in 1861 than it had been in 1776. The Southern states never sought to rule over the Northern states in the same way that Washington never intended to march into London, depose George III and proclaim himself king. The much more accurate term for that conflict is the War for Southern Independence. That's what it actually was.....a war of independence.
It comes down to 'independence' and 'defending slavery'. Independence brings up the subject of states' rights, which Lincoln pretty much obliterated; the South became a plundered war zone for decades.
Slavery almost certainly would have declined over the next half a century anyway; historically that institution was destined to minimalize.
Who can say what the outcome would have been if Lincoln had not decided his principles merited spending the lives of tens of thousands of people. Depending on ones POV, Lincoln was either a stalwart or a monster. As I say, historians write the text of any story.