If a student said she thought you were the worst teacher he/she ever had, how would you react and what would you say?

First of all I should NOT become reactive to this feeling.  I should try and get to know the reason.  If student is brave enough, she will tell me the reason, if I ask.  However, this is unlikely.  Thus, it is better to engage a colleague (preferably female) and get to the bottom of her feedback. After the feedback or real reason is known I will take appropriate steps.  The likely actions are: I will change and become better, or change her (because she has probably NOT seen the world as much as I have) or counsel her with parents to understand the reality.  There might be some funny reasons (such as my look, dress sense, habits, bad breath /odour, religious outlook, eating habits, etc.) if any need to be handled differently.

I WOULD ASK ABOUT THE REASONS WHY SHE IS SAYING THAT...

Positive.

Try to listen what did she find not good.