The main issue roots down to a very specific shift in creative direction when Friendship is Magic was created. Specifically this relates to the fact that the new director attempted to make the show enjoyable not only to the sterotypical little girls known to watch previous iterations of the My Little Pony franchise, but also to their parents. Since she realized that they would probably at some point have to sit down and watch the show with their kid, she didn't want them to have to hate sharing time with their kids by doing what previous seasons had done and form the content of each episode only to appeal to the sterotypical little girls. This is where the important matter lies; Friendship is Magic was designed to be a family show, not just a young girls show.
Now on to the more specific matters, making it a family show means it has content enjoyable to adults, but may be over the younger audience members' heads. For several good examples, this is something that almost defines the animated Disney classics such as Lion King and Beauty and the Beast. Now appealing to adults also means it will have content that appeals not only to the mothers watching the show, but also the fathers, and this is where the brony phenomenon begins. If the show was made to be enjoyed by 20/30-something year old fathers, does it not stand to reason that 20/30-something year old single men might also find the same content appealing, and by extension any man?
Alot of what makes the emergence of the Bronies as big of a phenomenon as it is is because of the previous mentality of "omg little girls stuff sucks" being shattered in the eyes of of the audience. The reason there isn't some huge explosion of Adventure Time or Regular Show communities (currently the two other most recently addressed animated series along with Friendship is Magic) is because they didn't do anything special in the eyes of their audience. While both of these shows, along with Friendship is Magic, are very high quality overall cartoon series, Adventure Time and Regular Show didn't break any molds and cater to a predominately male audience, so of course nobody is going to say that grown men watching them is odd, while grown men watching Friendship is Magic is going to seem outlandish because of the misconception that this iteration will follow its franchise's roots as a little girl's show. Breaking past this misconception and "awakening" to the idea that you can't take things at face value is what caused the original bronies to spread the word, exponentially compounding this growth as each new member felt the same "awakening."
As to what elemtents specifically make us enjoy Friendship is Magic so much can typically be said of any other worthwhile animated TV series. It has a strong sense of humor, with a well-defined and relatable cast of characters, with messages that resonate with the audience without being heavy-handed in their delivery. We enjoy shows such as Dexter's Laboratory, Ed, Edd, and Eddy, Hey Arnold, The Fairly Oddparents, and Phineas and Ferb for exactly these same reasons, so why should Friendship is Magic be considered less respectable or enjoyable simply because it has the title My Little Pony in it? When you learn to accept this idea, and look past the misconception that certain shows are restricted to only be enjoyed by their specific target audiences, then you will come to understand the Brony phenomenon.
TL;DR: I promised an essay didn't I? Now stop reading this and read the actual post you lazy bum