I'm sorry I am so slow in responding, especially because I really appreciate the question; thank you very much for that
However, after such an introduction one would expect a clearer response than I am able to give. I'm always awkward with such superlatives as "favorite... whatever", but there is no denying that the American Civil War is a chapter of history that captured my interest in particular. I feel unable to name one determining factor that sets it apart on my interest scale, but there are quite a few factors that I believe may each have contributed to this.
The American Civil War is but one of many parts of US history which I find especially interesting because they show so well some of the discrepances between ideals and realities in American history. It is not like the Civil War came suddenly up out of nowhere (in spite of the neo-confederate propaganda that interprets it as a sudden rush of aggression from the north fostered by the new republican party) but to study the roots of the Civil War one must go back much further and see which political (e.g. decision to maintain slavery in the new founded US though there were serious attempts to get rid of it in 1776), technological (the cotton gin of 1793 pretty much put an end to the hope (though the claim remained) that slavery would soon outlive itself and disappear on its own accord), legal and other stepping stones were laid out on the way into civil war. Even here we often have the discrepancy between ideals and reality (and they come with some masterpieces of rhetoric). Beside politics and rhetorics there is the sheer brutality of the struggle even before it officially began. Whether we are talking of the frequent abuse of slaves, about senator Preston Brooks clubbing Senator Charles Sumner into unconsciousness inside the US Senate, or about Jayhawkers and Bushwhakers murdering each other in Kansas and elsewhere foreclosing the actual war.
Then there is the actual war of course which in many ways is of particular interest. The dimensions were far beyond anything America had seen up to that point. It was a clash of outdated tactics of marching in close ranks with the very technology that made these tactics obsolete (the minie ball in particular). In many ways the US Civil War can be considered both the last large scale "old war" and the first large scale "modern war". Technology like the telegraph, and railroads played a major role in this war as well as the tactics of "burned soil" which saw horrible come backs in the wars of the 20th century. Many other inventions like the ironclads, submarines repeating rifles, and machine guns saw their first effective use in this war even though in many cases it was more like testing (machine guns for example were used on some occassions but not on a scale that they can be justifiably assumed to have had a significant effect on the outcome of the war).
An additional moment of tragedy is added to the US Civil War by the many cases in which soldiers from both sides knew each other or had even been close friends (having been in West Point together, having fought together in the Mexican War, or even being close relatives).
In spite of the fact that no other nation joined the war (though some clearly allowed for this "distraction of the Americans" to take more aggressive steps in their western hemisphere foreign policy (like the French in Mexico)) it was still a war fought by people from many countries. Newly arrived immigrants who saw no alternative but to become soldiers as well as immigrants who had arrived only years before. There were hundredthousands of Irish and Germans among the armies of the Civil War and also significant groups from other nations.
With all that there is yet another aspect that makes the American Civil War interesting, namely the fact that on a different level it is still going on. The struggle for the interpretation of the war is far from over. Lies like for example the claim that slavery had "nothing to do with the Civil War" become ever more accepted among certain groups especially if true points (like the fact that only about a quarter to a fifth of the population in the south owned slaves) are added to it to allow for the lie to appear more credible. The modern interpretations and falsifications of this war (often fostered by the "lost cause") are a very current topic, especially if one takes a look at how the war is presented, glorified and falsified in the movies which more than anything else seem to influence the view of people about the war these days.
These are some reasons why I am interested in the Civil War, but same as with LBT I don't have one ultimate decisive reason. A very interesting question though