I dunno if this counts as a "misunderstanding" per se; but I never ever went through a phase where I thought boys had "cooties." I always liked hanging out with them just as much as with the girls; and I was also a notorious flirt even at a very young age. I had "boyfriends" in kindergarten, and would make these boys sit next to me at snack time and hold hands with me, and I would tell everyone that so-n-so was my "boyfriend."
My parents and kindergarten teachers all thought this was hilarious. The boys tolerated it, because usually after a good sitting-by and hand-holding session at snack time, I'd really put out and go play Star Wars with them on the playground. Every man's fantasy, I know.
My girlfriends were confounded by this: "Ewwww! Muse! How can you play with Patrick?! He's got coooooooooooooties!" They were utterly scandalized, but I just never saw the logic in "cooties." What the heck was a cootie anyway? I remember looking very closesly at boys' skin, faces, arms, legs, trying to see if I could spot a cootie. And since playing Star Wars and Transformers with them was fun, and I never got sick or anything from it, I figured my girlfriends were just being snobs. Besides, all they ever wanted to do was play stupid dolls.
Although playing dress-up with the girls was fun. As long as I got the long pink princess gown and the biggest tiara in the box.
Contradictions abound.

This fascination with boys continued all through my growing up. I was the big heartbreaker all through elementary school, and I spent most of my recess time chasing boys. Of course I never thought about what I might do if I actually caught one--it just never occurred to me to plan beyond the chase, I suppose. Thankfully I never had to worry about it since they were all too fast for me (apparently I had cooties). My girlfriends would always tease me and say I was "boy crazy" and I would just shrug and go, "Yeah?" as if to say, "Isn't everybody?"
Kind of like when my classmates would tease me for having a large vocabulary by saying, "Ha ha, you probably read the dictionary," and I'd look at them nonplussed and go, "Uh huh." (Doesn't everybody?)
By middle school and high school I was quite the gregarious flirt. It started to suck once the boys started to like it and respond, because now I was responsible for hurting their feelings if I rejected them. That sucked, because I'm a really gregarious person and I like making people happy. Now that my friendliness was actually hurting people, hoo boy. I had to come up with a new strategy. I have always been boy crazy but ironically, I've never been a ho.
At the risk of oversharing,
I was a virgin until I was 24. And not for lack of trying by my boyfriends.