Why? The characters have a depth to them that is rarely seen in a cartoon, or even most of the more mature entertainment fare out there, the animation, while simple, is extremely well done (and from a technical standpoint is pushing the boundaries of Flash animation beyond what most people thought was possible) and to top it all off the the characters are relatable.
The main cast represents six different paradigms of self: A couple athletic types, one of whom has an insane work ethic, the other is talented but lazy. A shy veterinarian, who is always working to overcome her fears and shyness. A fashion-obsessed artist type who tends to bite off more than she can chew, especially when it comes to making her friends happy. A spacey party planner who often takes things too far, but is always there to lighten the mood and remind the others that even in the darkest of moments, there's always something to laugh about. And a finally, a neurotic perfectionist student who often prefers the company of her books to other ponies, and is obsessed with pleasing and living up to the expectations of her teacher and mentor.
No one character is ever depicted as being better for having a set of traits the others don't have, and they ALL have very real and believable character flaws. The stories are character driven and while episodic, there is continuity and over the course of the series you get to see the characters mature and develop. And along with all of that, it's cute and funny and somehow squeezes in some mature themes.
The situations are familiar and the challenges faced by the characters are also highly relatable:
Everyone has had deadline anxiety, or been over the top with worry that their friends didn't like them anymore.
Everyone has had a big event/convention/party that they've looked forward to for months, only to have it fall flat on it's face for whatever reason and not live up to their expectations.
A lot of people have had their pride get in the way when tackling an insurmountable task and forgotten (or refused to accept) that they have friends that they can call on for help.
Many people have had to deal with being too wrapped up in school and study to go out and make friends, or been unsure how to approach people TO make friends.
And who in their lives HASN'T, at one time or another, had to deal with choosing one friend over another to take to a special party? Or had two friends who had opposite and clashing personalities who you had to help find a middle ground when all three of you tried to do something together? Or had to find your place as the new person in a group that you just didn't fit into? Or faced the demons of their past in school when you had to return for an event or reunion?
There are plenty of "classic" cartoon moments that hail back to the old Warner Brothers cartoons that I grew up with, plenty of subtle pop-culture references and enough in the way of mature jokes (that a lot of kids just would NOT get) that even the most stoic adults that I've watched it with still smile quite a bit.
TL:DR, it's not for everyone, but those who do enjoy have very real reasons for doing so. It's not just another internet meme, or a rebellion against trolls, as has been insinuated.