The theremin is not like traditional instruments because there is no established, universally accepted way to play it. There is no "right way" or "wrong way" and everybody has their own ideas about to approach it. Never take any advice on how to play the theremin from anyone whose playing you have not heard, and NEVER take lessons from anyone you do not want to end up sounding like.
Clara Rockmore, the greatest theremin player who ever lived, once said "If you want to learn the theremin, you must always know where you want to end up before you start out".
The kind of music you will be able to play accurately and consistently on the theremin will be largely determined by the technique you are using. If you learn to play using a method that is not suited to the sort of thing you want to perform, you will hit a brick wall and have to go back and start all over again.
I know because that's what happened to me.
The best thing to do is to imitate, to the best of your ability, the playing of your favorite thereminist - and keep on doing that until your own unique style and musical personality begin to emerge on their own.
The important thing to remember with the theremin, an instrument in which EVERYBODY IS AN EXPERT, is that everybody is not an expert.
"People expect to go over to the theremin and IT PLAYS. No! It takes hard work, sensitivity, sensibility....attention to detail. You have to learn it and it's not easy. The music comes from the heart, the mind, and years and years and years of the study of music." Clara Rockmore