I copied and pasted this from my experiences listed in this post on Fimfiction, because it'll just take way too long for me to type this out otherwise. Technically speaking I don't call myself a "brony", per se, but this is still a good place for me to talk about how I became interested in MLP in the first place, so there you go. >^_^<
--------
Throughout my life, I avoided My Little Pony like the plague. Part of this was because I was always under the impression that it was aimed solely at girls, while the rest of it was because--if my online handle wasn't enough of an indicator--I preferred felines over equines (as an example, I became interested in Sailor Moon as a kid solely because of Luna and Artemis). I never really felt comfortable getting involved with MLP; I didn't even know that successive generations were a thing.
That started to change in late 2014, early 2015 or thereabouts. I'd been obsessed with Touhou Project-related stuff back then (and to a lesser degree still am), so when I heard about then-Screw Attack's One Minute Melee between Sakuya Izayoi and Dio Brando, I went to watch it as soon as I could. When I followed this up with watching reaction videos, I started noticing not just that several who'd seen that particular fight were interested in MLP, but also that "Starscream Vs. Rainbow Dash" was a thing.
So I watched the fight, watched reactions to it on YouTube (most notably those of Shanmul1995 and DYWTBA_Brony), and gradually became interested in what I was seeing. At this point, I decided to test the waters a little bit and checked into a certain set of fan animations (and reactions, of course) I'd heard about through TV Tropes but didn't look at too closely. It wasn't guaranteed to be factually accurate, but it would still give me an inkling of what I was getting into.
Turnabout ever-loving Storm.
I was on to something here. I continued reading stuff on TV Tropes about the show and recaps of the episodes, seeking out stuff that would interest me. I kept myself limited to stuff that I found either cool or funny (the latter mostly revolving around Pinkie Pie, as expected). The major downside to this, of course, is that due to my fairly narrow search criteria, the bulk of the episodes I haven't touched; the 100th episode is the only one that I've sat down and watched from beginning to end, if only because I like it when secondary/background characters get more fleshed out in personality.
Admittedly, this is why I don't call myself a brony. To me, being a brony would require a certain dedication or obsession with the show that I lack, being willing to maintain an interest in MLP that at least surpasses just casual observation, and I don't have that. When it comes to entertainment, I prioritize cats, professional sports (the Detroit, MI-area, to be more specific), and Touhou over almost everything else.
-----
There's a lot more that I didn't mention, but you're welcome to check the link up there if you want to read the whole thing.
As an addendum, I'm not quite as addicted to Touhou as I used to be, and I've gotten a bit more into MLP since then (I'd have to, if I wanted to write halfway decent fanfiction).