I really dislike the phrase, too.
Sadly, people rarely want to actually know how you are feeling or how your life is going. NT's use "how are you doing" as a polite, nothing, throw-away statement; a conversation starter or filler. It's the equivalent of saying, "Hey." as a salutation. ...Unless they are your boss. Then they do *not* want you to just say, "I'm good, how are you?". In fact, a manager or supervisor will get quite bothered by that response because when THEY ask "how are you doing" they want a status update on anything you are doing that is important to them. It took me years to finally learn that one (& advice from a NT person) , but now when I'm asked, "how are you doing" I reply with, "oh, the X project is done, but I'm held up on Z because Y".
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“For small creatures such as we the vastness is bearable only through love.”
―Carl Sagan