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?