As a boy, Benjamin Franklin was sharpening tools in his father’s yard when a stranger carrying an axe came by and praised the boy on how good he was with the grindstone.
He then asked Franklin if he would show him how it would work on his own axe.
Once his axe was sharpened, the stranger simply laughed and walked away, giving young Franklin a valuable lesson about people with “an axe to grind.”
We say that someone with a hidden agenda has “an axe to grind”.