[Grammar] Growing up, my family was vegetarian.

[jutfrank]

It is nevertheless illogical and grammatically wrong.

Well, I wouldn't describe it as either.

I do understand your point but the sentence should not be taken out of context. There is almost no way it would be interpreted that the family was growing up. And even if it were, there still wouldn't be anything illogical about it (depending on what you mean by 'illogical').