What every admissions essay has in common.
Some say there are but a few, basic stories that get repeated over and over. For example:
Boy meets girl and it either turns out well (Pretty Woman) or not (Romeo and Juliet)
Hero saves family/city/country/world (pick your franchise for this one, from James Bond to Star Wars) or not (Independence Day)
Mastermind criminals get away with it (Ocean's 11) or discover crime doesn't pay (Scarface)
You can come up with lots of examples for each of these categories. But if there are so few story types, what keeps us reading them, listening to them, and watching them? It's how their told and put in new contexts. Romeo and Juliet, the tale of young lovers from feuding families, was transformed into West Side Story as a tale of young lovers from rival gangs and then into High School Musical as a tale of young lovers from different cliques.
It's what you as the writer do with a basic story - and how you tell it - that makes all the difference.
That's true with admissions essays, too. There are only so many reasons people want to go to a particular school (great faculty in your area of interest, legacy, rigorous or flexible curriculum, etc.). So if you're asked a version of that question in a supplemental essay, remember that it's what your reason means to you - and how you express it in your own voice - that counts.
There's no formula for telling your story, but there's one overriding principle you'll find in all great stories: you have to speak your real emotional truth. If you write about something you wanted and didn't get, talk about the pain or disappointment you felt and, perhaps, how that motivated you to rebound. Readers can relate to that. And they can tell when you're holding back. Go deeply into the experience. If it's important enough to mention in your essay, the reader will want to know why.
At the end of the day, readers are most sympathetic when they see why you did something, how you felt about it, and how you reacted. Our default mode is to root for the character we're reading about as long as we understand their motivations and feelings. We're even able to like characters who do despicable things, like Scarface, when we see their emotional truth. And if we can be on their side, we'll certainly be on your side when you tell us honestly about yourself.