Okay, this seriously needs to stop.
To the people who ask how someone is doing, only to immediate attack their, "I'm good," statement -- to the people who dust off their pseudo-grammarian caps and go, "Don't you mean I'm well?": Cut it the fuck out. Because you're wrong.
Let's break it down: "good" is an adjective. "Good" is not an adverb. Which is why saying, "We want to do good on the exam," is grammatically incorrect. Instead, we use "well", because "well" can be used as an adverb, as in, "We want to do well on the exam so we can get a good grade in the class."
Now, let's get back to that, "I'm good," statement. You asked how that person is today. Since you were so busy patting yourself on the back about correcting your friend's grammar, you probably didn't notice that, by asking, "How are you today?", you were asking about their state of being. And when said person said, "I'm good," they are letting you know that their state of being is good. And "state of being", while a fun, abstract concept that can send any philosopher and psychologist alike into a lifetime of research and debate, is, for all intents and purposes, a noun.
And what do we use to describe nouns? Adjectives.
Crazy idea, I know! "Good" is not an adverb, and yet we can still use it as an adjective. Someone alert the presses, because this news is going to rock modern society as we know it.
Think of it this way: "goodly", while a horribly outdated word, is still grammatically correct. It can also be used as an adjective, but that's a convoluted tale for another time. Imagine how ridiculous you would sound if you corrected a friend's "grammar" by saying, "Don't you mean, 'I'm goodly'???"
You could say, "I'm doing goodly" and be grammatically correct, although you'll definitely get a few looks from the people listening to you. By the same token, "I'm doing good," is grammatically incorrect, unless they're trying to tell you they are doing good deeds and got lazy by the end of the sentence.
However, this is not to say that "I'm well," is incorrect. It just means, "I'm the opposite of sick," in this instance. And hey, sometimes people really want to let you know that you won't die of the plague by being around them. That's good info to know.
But, all joking aside, let's really get at the meat of why you are correcting your friend's grammar -- and correcting it incorrectly: you are taking a usually-innocuous set of pleasantries as a chance to prove how "intelligent" you are. You're not hoping to educate them on an important matter. You're not hoping to help them sound "smarter"; you're hoping to show them that you know something that they don't know. And the part that really gets under my skin is that you didn't even take the time to go on Google for 10 seconds to make sure you were correct. You were too busy congratulating yourself for being smart to actually look into the matter in the first place.
And regardless: unless you're part of the Totalitarian Grammar Society and your club is having a cocktail party, there's no reason to be correcting anyone's grammar in day-to-day conversations. Who cares if your friend or family member responded with, "I'm good," or "I'm doing good," or "I'm a goodly-good-good-doer with good on the goodly mind!"
Okay, that last one might be a sign that they're due for an evaluation. But aside from that, there is genuinely no reason to nitpick. It's the same reason why I bite my tongue (and silently hope that they'll eventually pay attention to that red dotted line under the word) when people spell ridiculous with an "e". Unless you're proofreading a paper or helping someone write a cover letter, it's mean-spirited to interrupt the flow of a conversation to "correct" someone. I don't care how good (or well/not sick) your intentions were; if you're willing to do that to someone you know -- or worse, someone you just met -- then, at least on some level, you consider yourself superior to them (or you wish you were superior to them in some way). The fact that you are incorrect in your correction makes it just that much worse.
So try it: next time you ask someone how they are, just listen. Even if, "I'm good," is just another insipid line in an arbitrary script that lets other people know just how social we are. Listen to them say, "I'm good," respond back if they ask how you are doing, and -- crazy concept, I know -- enjoy their conversation and company.
Because, seriously, the next person who tries to "correct" my grammar is getting the boot. Or, since the weather is finally warming up, the flip-flop.