I've always been a picky eater, and I can attest that I have never, ever used food as a means for a power struggle or to control someone (not as a parent, not as a child). In my experience, the power struggle is far more likely to rest with the parent.

If I didn't or don't want to eat something, it's because I simply don't want to --- either because it might make me sick or feel unwell or because I just don't like it. I'm not allergic to much of anything --- I have intolerances, and they're completely different from allergies. Other people here have said the same.