This question is surely debatable, partly because it can be looked at from two directions. One approach would seek to offer the most direct and clear-cut answer by identifying the fewest causes, or perhaps the single factor of the slavery issue and the inability to solve it through peaceful methods. The other would identify many individual causes. It's somewhat arbitrary to specify "three" as the number to be settled on, but working within these limits, and establishing the premise that slavery was the overall cause, I would identify the following as individual factors:
First, the enormous growth of the abolitionist movement and the publication of important literary works, not only Harriet Beecher Stowe's Uncle Tom's Cabin but books by African American authors such as (to name only two) Frederick Douglass, in his Autobiography, and William Wells Brown, in his historical novel Clotel, which deals with the African American family of Thomas Jefferson. Many people who had been indifferent to the practice of slavery were galvanized by these books into seeing that slavery was a moral wrong and an embarrassment to the United States, with its proclaimed values of liberty and equality.
Second, John Brown's raid on Harper's Ferry, VA in October 1859, and Brown's execution is set for two months later. The attempt to foment an uprising of enslaved people caused Southerners to believe that they were not going to be left alone in peace to practice their "peculiar institution." The Southern militia system, which up to this time had practically been non-existent, began systematically to be built up and became the nucleus of the Confederate armies a year and a half later. In the North, even people who were not necessarily committed to abolition saw Brown as admirable, a martyr for the cause of justice, and this had the effect of increasing the anti-slavery feeling in the North.
Thirdly and decisively, the election of Abraham Lincoln as president in November, 1860. Lincoln personally, and the Republican Party to which he belonged, declared unequivocally that slavery would never be extended into the territories of the United States. No previous president or administration had taken this position. The Southern leadership knew that, with the vast territory of the States eventually to be organized into free states, there would be, first, a drop in the "value" of enslaved people, and second, an outnumbering of the slave states in Congress and thus an inability to advance any agenda in favor of slavery. In December, 1860, South Carolina seceded from the Union, and the other states that would form the Confederacy followed in the next few months. This led directly to war, given that the Lincoln administration was not going to abandon the federal installations in the South or to acknowledge that the secession of those states was constitutionally legal.
Through the decades, many have advanced the notion that other issues, involving economic factors such as tariffs or the desire for an abstract ideal of "state's rights" were the actual cause of war. None of these explanations can be sustained. Southern leadership itself, in sending commissioners to those Southern states still in the Union in order to urge their legislatures to vote for secession, made it clear that their concerns were rooted in their fear of abolition and that it would destroy Southern society. Though other specific events and factors leading to war can be identified beyond those discussed here, all of them are rooted in the slavery issue.