I took ballet for four years, but mom eventually pulled me out over my protests because according to her I wasn't improving.
I also wanted to do gymnastics (I'd love to be able to pull off those flips!) and judo, but was told no, it was too dangerous and in the case of judo that it was "only for boys"...yet she allowed me to take karate. Then again, she also liked to encourage me to do more "girly" activities like dance if I expressed how much I liked to do something like fencing or the aforementioned martial arts. 
Did you take karate? (Maybe she didn't let you take judo because you'd be grappling with all those boys
).
Yes I did, long enough to earn a black belt.
And the funny thing is? We did some grappling there too (though probably not as much as you'd do in judo). And yes, I think that might've been the reason.
I also had the chance to take other forms of martial arts later, which kind of makes up for that, I suppose.
Off Topic, in defense of Rockie's mother; post continues on topic afterwards. 
I did Tae Kwon Do and also tried a few Judo classes (liked it, but didn't have time to do both). In TKD, we practiced throws a decent amount, but it was generally part of the self-defense part of the class (i.e. not really classic/traditional Tae Kwon Do, just good techniques to know). Judo was a whole different story. As in "I just met these guys 15 min. ago, and now we're jumping over each other leap frog style/crawling between each others legs during the warm-up, followed by rolling around on the floor grappling with them for another hour or so." One of the fighting positions we used a lot during those few classes involved one fighter (on their back on the ground) holding the other off by wrapping both legs snugly around the other fighters waist; many techniques also involved grabbing the lapels/collar of the opponent's uniform/shirt (chest/breast area) and using them as a point to pull on or hold the opponent.
Like I said, it was really fun, but even as a college student who was already used to getting "up close and personal" with my martial arts classmates, it felt a little awkward at first. I can see how a mother (or father) could be understandably leery of her daughter practicing judo with a class full of boys, especially if she wasn't
really certain that her daughter would be assertive about cutting off any inappropriate contact. Judo practice kind of blurs the line of what is "appropriate touching," which might make it harder for a kid to know when to object. I was an adult when I tried it; if any of the guys had made inappropriate comments/tried to grope me/etc., I would have had no problem telling him off, refusing to practice with him again, telling the instructor, or whatever other action was needed. A kid might not be that assertive.
That said, it still doesn't make judo "only for boys." Nor am I arguing that girls shouldn't join judo classes with boys, just that there might be some justifiable parental worries.
Back on Topic:One of my university friends started a small bellydance club, and I later continued taking it in an official class. Based on my experience and seeing the other students, bellydance is one of those activities where almost everyone is going to feel like they stink at it at first. You get asked to isolate and exercise muscles you didn't even know you had, and once you get enough of the moves down, you start layering them (doing different moves at the same time), at which point even the moves you could do well start falling apart again. If everyone dropped out when the didn't think they were dancing well, I bet there would be very, very few bellydancers.
One of the students in our first little bellydance group was the instructor for the judo club. An older, stocky, muscular man who practiced with us in his judo uniform (complete with black belt). Was he naturally brilliant at bellydance? No, but he stuck with us until our teacher moved away and the club ended. The rest of us loved having him in the class. There's something incredibly sweet about seeing this tough martial arts instructor in his gi and black belt very intently watching himself in the mirror as he tries to make his hips move the right way. Especially since he was so obviously having fun. Sadly, he didn't try to join the official bellydance class that got started, because "the other [young, female] students might get the wrong idea."