[DrewDevil]

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it seems rather arbitrary which points of grammar people get upset about.

for example, when asked "how are you doing?" most people respond "good," and few would fault them for this even though "well" is the more grammatical response.

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That's crap.
"How are you doing?"
"(I'm doing) good"

good = predicate adjective

That makes more sense than "I'm doing well." "good" describes the subject, whereas "well" describes the action. "I'm doing well" is akin to "my ability to be is good", which is just sort of weird.

It's like people who say they feel well. I wonder what would happen if I burned off their fingertips. They'd probably feel pretty bad and badly I suppose.

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Sorry, but "I'm doing well" is the correct response.

"Do" is not one of the few linking verbs that take an adjective. They are:

is/are
become
seem
feel
appear
look
taste
smell

Every other verb takes an adverb.