I'm not sure but I suffer the same affliction. I have also tried to train myself to raise the right one on its own but it is very difficult. My friend can control each eyebrow indepedently whch annays me but least it is not an essential life skill.

This was my predicament as well when I was younger. (I'm right-handed as well, by the way.) I had time to spare, so I stood in front of the mirror and tried to replicate the effect on the other side of the face, i.e. with my right eyebrow. Through some practice I managed it, and soon became better at controlling it than with my left eyebrow. Now the effect has evened out, and both are equally obedient. I haven't had the same thing in any other muscle, so I cant say if this is an isolated incident. I can't say either if this is some feature of my brain's left hemisphere, being able to replicate the right hemisphere's actions, or if my young age at the time was a factor. (It might be that I've got the sides jumbled up, it's been a while.)

But if you want to learn this, I suggest you just stand in front of the mirror and try to.

I can't find any literature on the single-sidedness of this ability, however. My guess would be that, since one only sees either one raised eyebrow or both, that one learns making the expression, and thus only does it on one side. Or that this is hereditary, and one has a bias toward making it on one side, leaving the other to be learned manually.

I can do both. I'm right-handed.

I can raise either eyebrow independently and am right-handed. However, I can only 'twitch' my left nostril...

It is all down to practice. When I was younger, about 12 I think it was, I could not flare my nostrils (rabbit style) however with practice, trying to imagine the muscles necessary to flare them, I eventually managed it and now can flare them rather adeptly. I never had such an experience with eyebrows, always been able to move them well, however I am better at moving my left one. I can now make it do a mexican wave (like the cadburys advert) from the left side to the right (see body-popping breakdancing). I'm right handed and can't do that with the right eyebrow. Yes, it is a fantastic party trick. I think some practice is in order for my other brow.