What does the word reproof mean within the context of this sentence? As for Ben, he was less afraid of a whipping than of his father's reproof. And, indeed, his father was very much disturbed.

scolding, disapproval, blame, reprimand

Any of these options would work. It is clear here that Ben is not as afraid of the physical punishment his father would dole out for his crime, but rather the verbal punishment. This often comes in the form of a scolding or reprimand. It shows that the father is disapproving of his son's actions, which is confirmed by the last sentence when it describes the father as "very much disturbed."

He didn't want his father's " disapproval"