I've been told that it's all about whether the word in question describes what/who a person is: a baker, a lawyer, an Italian, a student, a grandmother... These words are considered adjectives when used with the verb "to be" - être - and also the verb "to become" - devenir (possibly others I don't know about), with the exception (there is always an exception) of "c'est/ce sont", where they are nouns and do take the indefinite article. - "il est étudiant", "c'est un étudiant"
I'm afraid you are quite mistaken. I will assume that you meant to type, "Il est un étudiant", but, as it happens, and has been explained several times already on this page, this is not correct. It is an exception to the usual form.
Words that describe occupations (boulanger, professeur, cuisinier, etc.) do not take the indefinite article (un, une). We say: "Il est boulanger; elle est professeur". And, as an additional wrinkle, "étudiant" is included in this category.
Because translation is more complicated than simply transforming one word at a time. One-to-one literal translation sometimes works, but often not, because each language has its own rules. In English, we use the article "a" in this structure; in French they do not use an article in this structure. This is the kind of thing we are here to learn.