As has been pointed out by Xachariah and Crux, perhaps you should think of "How are you?" as a set of symbols with multiple potential meanings rather than one whose meaning is determined by its literal interpretation.
Consider (yet another) analogy: homonymy across languages. Imagine that the sound "yeridan" refers in Language A to a puppy and in Language B to an army of bullet ants. If a speaker of A asked you whether you wanted to hold a yeridan, you might answer that you would, while you surely would decline if the one doing the asking were a speaker of B.
Similarly, we have (far more than) two languages, or registers, at work here. One is the language of social grace, to be used when signaling certain aspects of our social situation (e.g., loyal to whom, intimate with whom, aloof toward whom). When conversing in this language, the function of "How are you?" is to initiate conversation and display basic good will. The other language is the language of intimacy, to be used when giving details about our lives to others. In it, "How are you?" functions as a query about recent goings-on and one's general situation.
The meaning of "I'm fine" as a response similarly differs depending on the context, just as the meaning of "Yes, I would like to hold a yeridan" differs depending on who's asking. Saying "I'm fine" in a social-grace context is just as truthful as saying "No yerdidans for me, thanks" in a Language B context, regardless of how one would respond in the context of intimacy or Language A.
I've seen an article on LW about Santa Claus and most people were very keen on not lying to their kids (and I agree). I have a little kid who is generally quite truthful, innocent enough not to lie in most cases. I noticed recently that when someone asks him, "How are you", he usually answers in detail because, well, you asked, didn't you? When I was a teenager I hated people who lied and I tended to ignore these unwritten social rules to the extent I could. I.e. I didn't ask if I didn't want to know and people thought I was rude. So, my question is, should I teach him to lie upon these occasions?
More broadly, I was thinking, why am I committed to being truthful, in general? I guess because I would hate to be lied to myself. This is a kind of magical thinking maybe, or maybe it's a part of the social contract. This sort of lying in fact promotes the social well-being because to answer truthfully creates an unwelcome burden on my interlocutor who asked out of politeness and is not in truth interested. But it still feels wrong to lie. Even more wrong to teach your kid to do so.