Just popping in to point out that there’s something known as a “flat” adverb.
Yes, and we might want to note as well that in closely related German all adverbs and adjectives are the same form anyway, so they don’t waste their time arguing about it. We can go through all these taxonomic gymnastics to justify (or condemn) usage, or we can just recognize that it’s not against the laws of nature to occasionally use an “adjective” where an “adverb” would occur, and that in doing so one can become the other, or vice versa. It’s not the end of the world.
In fact, we might just want to realize that language is much more complex than the labels of the parts of speech would allow.
He learned that “badly” is correct in grammar school.
Right. That’s why linguists construct isoglosses which attempt to describe regional dialects; they’re the actual experts, and they’re being more descriptive than most dictionaries, which have neither the space nor the expertise to go in-depth on what words are used where any more precisely than country or very broad regional descriptions.
So, basically, descriptivism is the standard in linguistics for all the same reasons it’s the standard in physics: It’s an object of study, not ignorant bias and bigotry.
Incidentally, “feel” in this context is what’s called a linking verb, and serves the same function as “be”. So “I feel good” carries a similar sort of meaning to “I am good”, or (to use a different linking verb) “I look good” or “I seem good”.
Let’s just say that historically, “I feel bad” is correct but badly has come into common use so much that it may also be considered correct. However, the doctor in the OP is still wrong if he is stating that “I feel badly” is correct while “I feel bad” is incorrect since everybody here seems to accept that the latter is still correct.
Also, nobody said that physicians could write or knew grammar.