Can Hogwarts Make a Mistake?

This past month has been a blur. I got my letter from a school of magic, Hogwarts saying I was accepted! To my family, it was unreal. You always look to your parents or, in my case "legal guardians" for answers, and when they have absolutely no explanation, it can be kind of scary. It should have made sense, like I've always felt like there was more for me, like this explained everything. I should have been satisfied. But something just felt amiss. I went shopping for supplies, I got a toad, Greg, and a wand (ten and one half inches, hornbeam, unicorn hair, relatively springy). It took like nine hours to get my wand. I must have tried over a hundred different ones that seemed to hate me. This wandmaker dude treated wands like they were people, like when I tried one that didn't respond as well, he'd say something like, "Oh, no need to be rude." I think in the end he just threw one in my hands and gave up. I should have been so excited, it should have been fun, should have been, could have been, wasn't.

So it's finally the big day. Of course, I sat by myself in a compartment on the Hogwarts Express. I was alone, again. The Sorting Ceremony was hardly better. I had to be first, of course, what with a last name starting with A. Abbott-Finnigan. Hermione Abbott-Finnigan. What kind of a name is that?  Abbott for my mom, Finnigan, my dad. I don't even know their first names. A little backstory on me: My dad died while my mom was still pregnant with me, and my mom died right after I was born. I was given to my mother's brother, who didn't really want another burden, so I now live with my father's neighbor's sister's uncle's brother's niece's cousin's friend and their five other foster kids, three cats, guinea pig, and parrot. I've always felt like just another thing in their house to be fed, walked, and given fresh water routinely, not necessarily given attention beyond that.

Anyways, I got sorted into Gryffindor. I have no idea how that happened. Gryffindors are supposed to be brave. I can't even see a tiny spider without freaking out and running out of the room, begging someone else to kill it. The Sorting Hat told me I could go into any House I wanted, I would succeed in all of them, and it was I who really made the decision in the end. So I told (well, just thought really hard) the Hat I didn't really care, I didn't belong anyways. I tried to keep that last part out, but when it can see into your mind, it's hard to keep out certain parts. My response from the Hat was just an ominous, "You'll see..." and a "GRYFFINDOR!" said aloud.

So I'm sitting in my four-poster bed, perfectly warm and comfortable, in the Gryffindor common room. It's now two weeks into the year. I seem to be one of Professor Slughorn's and Professor Longbottom's favorites. I do love Professors McGonagall and Flitwick, although I cannot perform any spells successfully. Maybe I am just a Muggle. I haven't cast one spell all year. That Rose Weasley who's in my year, House, and classes, can do everything, so it's not like it's impossible. Is it possible that Hogwarts sent a letter to a Muggle by accident? Did Hogwarts make a mistake?