"Он не вегетарианец."
Перевод:He is not vegetarian.
Welcome to our course :) The thing is, when you use clever tricks to convey emphasis and emotion, to fine-tune your speech to better express your point, you better be pretty well sure what you are doing.
A native speaker or a proficient user of English knows that "He is no vegetarian" is a grammatically valid version of "He is not vegentarian", just stronger in tone. However, teaching how to use these variations appropriately—and explaining when NOT to use them are waaay beyond the scope of this rather basic course. For a non-native beginner accepting "no vegetarian" here means that in English "no" and "not" are the same thing, and that's just not true.
Please accept that English used in this course is way more precise and to the point, while Russian allows huuuge variation, to the point I doubt a native speaker could ever use it unless in this course.