The lady doth protest too much, methinks.
— Gertrude, Hamlet · William Shakespeare
I think she's insisting so hard that it gives her away.
Watching a play within the play, Gertrude judges a queen's over-the-top vows of loyalty as unconvincing. The line has entered everyday speech to mean that too strong a denial can be a confession — the harder you insist, the less you're believed.