why is wrong to answear "I'm doing good" instead we should answear 'I'm doing well'
Colloquially, "I'm doing good" is said, heard, and used. In fact, there are some dialects of English in which "I'm doing well" isn't even a choice. It's "I'm doing good." The shift from "well" to "good" is related to meaning. For some speakers, "well" tends to express health, whereas "good" express (physical and non-physically related ability; e.g., They are good writers ~ They write good. Now, the last example wouldn't be considered Standard English, but nonetheless it's said, heard, and used by a majority of speakers within certain English dialects.
As for the Standard, "well" tells us how you are doing, it's an adverb, whereas "good" describes the quality of someone or something. It's an adjective.
Given the sentence "I am doing _____" and the choices "well, good", pick the adverb. "well" is an adverb. It adds meaning to the verb "am doing". That's the Standard.
Hope that helps.