Anyone who scolds you for saying "I'm good" is the worst kind of grammar bully.
This article satisfies Squid Commo Objective #2: Suffer not bullyery.
Describing yourself is done using the construction I + am + adjective. Good is an adjective. "I am good" is as proper as it gets.
So what's the problem here, people?
The problem is this lowest class of grammar bully, who not only wants to browbeat others in a vain attempt to raise itself up, it doesn't even understand what that criticism should be.
The original complaint is when people use good adverbially. Instead of saying, "I'm doing well," people say, "I'm doing good." That's technically improper English.
But these idiots don't understand even that much. So they perk up when someone says, "I'm good," and release the lame banshee of malinformed indignation.
Ugh. They're the worst. The absolute worst.
Ignore them. They have no interest in correctness. They're in it strictly for the bullyery.
You want to speak like a grammar bully? Try these fun expressions.
How are you?
Master Squid: I'm good. Better than I deserve.
Bullyery: I'm well. Weller than I deserve.*
How are you doing?
Master Squid: I'm doing great.
Bullyery: I'm doing greatly.
__________
* Well, that's just silly. Everyone knows the bullyery wouldn't say "weller." They'd say, "more well."
Are you being good for grandma?
Master Squid: Yes, I'm being good.
Bullyery: Yes, I'm being well.
See you later.
Master Squid: Take it easy.
Bullyery: Take it easily.