As you've told the story, it's puzzling. I don't understand your teacher's reaction. I'm a U.S. speaker and "What a shame!" seems fine to me, and quite natural. I am checking the dictionary definitions at ahdictionary.com's definition, in the phrase "What a shame," the word "shame" has meaning 2b: "A regrettable or unfortunate situation: 'It was a shame how the place had fallen apart, with tall scorched grass and sagging gutters.'" To me, it does NOT mean dishonorable, disgraceful, or wrong.

You're right. "What a shame" does mean "what a pity." I can't imagine why your teacher would be truly upset!

With certain intonation and facial expression, "What a shame" can sound uncaring, as if you are being sarcastic saying, "That is not a problem."

It all depends on the tone of voice you used. The words can mean, "I'm sorry that happened." or "You deserved what happened and I'm not sorry at all."

Hmm here's my two cents: Oxford dictionary definitions: PITY: - A feeling of sorrow and sympathy caused by the suffering of others. - A cause for regret or disappointment SHAME: - A painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behaviour - A loss of respect; dishonour - A person, action, or situation that brings a loss of respect or honour - A regrettable or unfortunate situation or action "What a shame" and "what a pity" are for the most part similar in meaning to most people. But look at the first 3 definitions of "shame" provided by Oxford Dictionary. While "pity" seems to focus less on the "loss of honor" meaning, "shame" seems to focus more on it (plus the "wrong/foolish behaviour" in the first definition has negative connotations). So since "shame" CAN have the meaning of loss of respect, dishonour, etc., "What a shame" could be misinterpreted by some people if you do not say it with the right tone, facial expression, body language, etc. That being said, when people say "what a shame", most of the time they mean it in the "what a pity" way, though. Only a very select few (including your teacher, it seems) would look too much into it and think of the less commonly meant meaning. So don't worry too much about it :) But maybe next time, just to play safe, say "what a pity" instead?