In these days, one engaged in the occupation of splitting hairs might very likely be engaged in some profound scientific work, trying, perhaps, to find some microscopic cause for the dividing of long hair at the ends.
But three hundred years ago when the phrase was coined there was no thought of scientific research; it meant to divide into exactly even amounts, so precisely as to afford no slightest advantage.
A hundred years later, however, it became an ironic figure of speech; one who would split hairs was one who would argue endlessly over fine distinctions, over differences of trivial importance, and this is the sense still in use.