Hat tip to Go-English
To protest too much is to insist so strongly about something not being true that people begin to suspect maybe it is true.
You do like that girl, don't you?
Answer: No! I don't! Not at all! Why do you think so?
Reply: You protest too much.
Protest too much comes from Hamlet by William Shakespeare; the Queen speaking: The lady doth protest too much, methinks. (Note: people do not usually use the word "methinks" when they are speaking English today.)
To protest too much is to insist so passionately about something not being true that people suspect the opposite of what you are saying.
Do you think he is telling the truth?
Answer: I think he protests too much.
Paul Flynn MP hath a blog, that doth protests the Labour Party's innocence of all charges of corruption ad nauseum