Why was the American Civil War inevitable?
I think a more appropriate answer would be that the Civil War was inevitable from the founding of separate colonies in the Chesapeake area and New England in the 1600's. The southern economy was agricultural because the area had good soil and long growing seasons which lent itself to large scale agronomy. This situation did not exist in the North, where thin soil and short growing seasons made shipping and manufacturing the only reasonable method of economic success.
Differences between the two arose not so much over slavery (although it was always the gigantic elephant in the room) as over issues such as the Tariffs imposed to protect Northern industry which were injurious to the southern economy. The first serious threat of secession from the South was the nullification crisis during the Jackson administration. It should be noted, however, that those who opposed the tariff feared that the federal government would one day arrogate to itself the power to abolish slavery.
So the two areas were so different from the outset that the Civil War (properly known as the War of the Rebellion) was likely inevitable from the founding of the colonies. The two areas were too different and evolved differently.
I wonder if you were supposed to be answering this question with reference to a specific year in history. In other words, should this question be "why was the Civil War inevitable in 1854" or 1860 or some other year? The closer we get in time to 1861, the more inevitable the war. In 1789, surely the war was not inevitable. After Lincoln was elected, perhaps it was.
If the war was inevitable, it was inevitable because the North and South had grown so far apart over time that they could never reconcile with one another. This separation started when the South developed the slave economy that was based on raising cotton for export. This made the interests and needs of the South very different from those of the North. Over time, the two regions each came to be more and more suspicious of the other. Each region felt the other was trying to destroy its way of life. If war was inevitable, it was because of this suspicion and mistrust, which made compromise and reconciliation impossible.