nits...

[No Name Available]

That explanation makes a lot of sense!  I wonder if it is the same nit, as in
"Get right down to the real nitty gritty"? Your explantion of  nitpicking as
'going through hair with a fine-toothed comb, looking for fur,'  might well
fit the definition (at least from my perspective) of the phrase, "nitty
gritty":  "the bare essential; the crux of the matter; the real/true purpose,
goal, intent, or motive."   After picking out the distracting features, one
can uncover the true, or ulterior, motive.  (Or, maybe I am trying to make a
connection that doesn't exist.)
                            PAT