"I'm well" vs. "I'm good" vs. "I'm doing well", etc

The greeting How are you? is asking How are you doing in general?

—

How are you?
I'm well. [Misunderstood the question.]

because well as an adjective which means:

in good health especially after having suffered illness or injury

This would be an answer to How are you doing physically, how is your health?

—

How are you?
I'm good. [Misunderstood the question.]

because good as an adjective means:

having moral excellence or admirableness

This would be an answer to

How would you describe your character, superman? I'm good.

—

How are you?
I'm doing good. [Grammatically incorrect.]

because good is an adjective, not an adverb.

—

How are you?
I'm doing well. [Correct.]

because well is an adverb describing how you are doing.

How are you?
I'm doing fine. [Correct.]

because fine is an adjective which means:

being satisfactory or in satisfactory condition

Why do so many people say one of the first three responses?

The reason people give the responses you label as “wrong” is because well and good have more meanings than the ones you cite.

Merriam-Webster, for example, gives definitions that make sense of the three examples you label “wrong”:

• For “I’m well”, there is well (adjective) 1b: being in satisfactory condition or circumstances

• For “I’m good”, there is good (adjective) 2e: free from infirmity or sorrow

• For “I’m doing good”, there is good (adverb) 1: WELL

So they all seem fine to me.

I think this question is harmful and offensive, as thesunneversets said.

The answers to the question "How are you?" that the questioner says are wrong are in fact all perfectly good English.

The questioner is grossly misinterpreting the dictionary by extracting one area of meaning and ignoring the rest. He simply doesn't understand the real meanings of the words "good" and "well".

The Wordsmyth dictionary gives this:

good [adjective]

definition 1: having qualities that are desired, enjoyed, or beneficial; desirable.
synonyms: beneficial, desirable, positive, well

Other dictionaries give something similar. "Good" is a broad term meaning what is desirable, well, healthy, positive, etc.

To the question "how are you?" the following are all fine and grammatical:

I'm well

I'm good

I'm fine

I'm OK

I just hope learners are not led astray by this question.

I'm really not so sure the first is incorrect. To say that you are well is, to my understanding, a correct way of describing your health.

I've never seen the use of "well" in that context formally corrected. Is it really wrong?

That said, I think many people simply exchange "well" with "good", whatever the situation.

If you want to take this narrow interpretation, then the question is wrong. It should be:

How are you doing? / I'm doing well.

You are, apparently, not interested in how a person is, because evidently all the common answers are not acceptable to you, but in how a person is doing.

In practice, no one really cares about the difference, but there is a fault in your question.

Why do they get it wrong? Perhaps sometimes because they're not really listening to the question. It seems to me that these sorts of pleasantries are often responded to by rote, which means the individual response is one of habit.

While I'll agree that the "incorrect" versions grate on the ears, the "correct" version is perhaps a little too prescriptive for my tastes.

Since you're probably the asker in these exchanges, perhaps a workaround would be to ask a question that is less likely to elicit a rote response. "How is your day going" or "How was your weekend" or something that would nudge the respondent to respond to the question you asked instead of just spitting out a generic response.