The reason for it is because everything about the show manages to work, even the sensitive topic of Relgion (WHich is amazingly downplayed). I hope it continues because a) I have seen Animes like this in calliber go to the 50th episode, or beyond, and B) there is lots of energy left over in the ending that indicates a continuation.
What works with this show is that there is none of those confusing anime cliches, and if they are any, they are not as potent as in other animes i have seen. I also love how relatable the main character is; if you remove the bit about him being a son of Satan, then whats left over is how the main character tries to fit in, even with his "Special status". I aslo find it intresting that the younger brother was the teacher, which added to the whole stress of fitting in, and in the third episode, there was this whole exposition scene where Yukio says that Rin is a threat to him.
If there is going to be a second series (I hope) One story arc that is from the manga that would be a nice series of senarios would be the whole senario where the Exwire's and a whole group of excorcist goes to Kyoto to investigate a breach in the branch there, and the whole senario leads up to RIn being sentenced to death for losing control of his flames, and not being able to draw his sword out of fear of hurting those close around him. WHile this is going on, Yukio fights his own little demons, while they fight off a massive demon. However, that is my honost opinion.
I have one problem with the series though, how quickly the students warm up about RIn being the son of satan. In the Manga, it takes a nine or so chapters, before the group gets back on good terms with Rin, and still they don't have complete faith in him (Even if he is the only one who can defeat the demon with ease) , however, in the Anime, it takes two episodes ( -_- ).