Notes on English usage - good or well?
To my British ears, the response of "I'm good" to the greeting "How are you" is discordant in the extreme! As I've said to people who have answered in this way, "I was asking after your health, not your morals"!
So what's wrong with using "good" in this sense instead of "well"? Basically, the difference between the two words is that "good" (in this context) is an adjective and "well" is an adverb. Remember that an adjective is a word that qualifies a noun (as in "a large house") and an averb qualifies a verb (as in "he fought bravely"). Many adverbs end in "ly" but this is not a universal rule, and "well" is one of the exceptions.
Therefore, if I ask you how you are, I am expecting a qualification of a verb, namely the verb "to be", not a noun. You should therefore use an adverb in your reply, not an adjective.
Just to confuse matters, "good" can also be used as a noun as well as an adjective, so there can be cases where "he did good" is correct! For example, if the context is the life story of a saint, you would not be surprised to find the statement, "throughout his life, he did good wherever he went" (as opposed to the biblical "he has done evil in my sight").
However, when a sportsperson, in an interview, says "we did good today" you can be pretty sure that they are not talking about how they have benefitted society at large, but should have said "we did well"!