Provenance
Where it comes from.
'Dr' abbreviates doctor, from Latin doctor, 'teacher,' and docere, 'to teach.' For centuries it named a learned adviser before it became, by the late 1500s, chiefly a physician. As a title it still carries that mix of expertise and trust.
'Neat' entered English in the 1540s from French net and Latin nitidus, 'gleaming, elegant, trim,' from nitere, 'to shine.' Its senses gathered around good order and tidiness. Put a shining, well-kept word behind a teacher's title and the name invents its own small, reassuring expert.