A long time ago I was unable to answer the security question for my AOL account. The account had been hacked and used for mass spamming. AOL would not close the account, or help me change the password (or stop the spamming) until I answered the question.

"...but the account is being used for malicious purposes." - me

"Sorry, sir but until you tell me what you named your first dog I cannot stop it." - AOL