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There could be many reasons. The context is not clear.
1. People are conditioned to be silent when they are  in  a clinic or in the presence of a doctor. from childhood we are told to respect doctors and not to make noise or talk in front of or, in the presence of, doctors.

2. We do not want the doctor to be in a bad mood or we do not want to disturb him/her as this is a question of health. and no one wants to get treated by an irritated doctor. we allow him/her to think in peace.

3. There is a white coat syndrome. Some patients are not able to speak properly with courage in front of doctors and they hide their diseases or symptoms.

Children especially or villages become quiet when they see a white coat man.

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