I would have thought that the answer to this question lies in the humanities or social sciences, rather than physics.
Physics of course can describe the quality of the sound produced by a theremin, but it cannot account for it's perceived "oddness".
I would punt that one of the reasons humans dislike sounds that are "too pure" is because they have a quality that is simply unfamiliar to the ear. And theremins (or sounds similar to them) have often been used in contexts that imply menace - such as in depictions of aliens landing.
But another way of conceiving the same quality of "purity" is that the sound lacks complexity, and therefore people find it easy to analyse, and in turn shallow and unstimulating. An instrument that imposes purity also means that players lack the ability to be "expressive" (a byword for subtle auditory complexities and variations) and therefore lack the ability to compose more satisfying pieces.
A related point on "purity" is that appreciation of music has a certain aspect to it which is related to the difficulty of production and respect for the skill of a musician. People may appreciate purity when they know it implies difficult-to-achieve precision, but less so when it implies rank simplicity and lack of difficulty.
Another thing I've noted about theremins is that they have an amplitude control that is unlike any mechanical instrument. They produce a sound that fades in and out as if someone has their hand on the volume control of a speaker - which of course is exactly how they work, but that gross control of volume is not a familiar technique in playing a musical instrument - and again, the control it exerts is "too pure".
As @Pieter notes in the comments, there is also a perfect glide between notes. Some instruments are fretless, but very few are played consistently in a fashion that gently blends between every note - most pieces of music have at least some sharp transitions.
A related point is that theremins tend to have no apparent "beat" (if played on their own outside a band of other instruments), and there tends to be no apparent percussive element to each note (which even fretless instruments can have on account of how they are plucked or otherwise played). Rhythm is an important and pleasing aspect of music.
Those are my off-the-cuff thoughts on the matter, anyway.
I would remark in closing however that perfectly good and pleasing music has been created with a theremin, with no apparent odd quality when it supports other instruments. "Good Vibrations" by the Beach Boys is an example - apparently, Brian Wilson used to refer to the theremin as "that damn woo-woo machine".