How did the Milgram experiment cause psychological harm?

The experiment is unethical and probably would not be allowed by today's standards. The biggest problem is the use of deception, which the experiment relies on. The scientist lies to the test subject saying they will be assisting in a 'learning experiment' and that the shocks are genuine, when in actual fact the scientist is experimenting to see their reaction to the instructions.

The scientist also told them at the start that they are free to leave at any time, but once the voltages increased and the test subject was placed under pressure, the scientist would 'prod' them by saying "You have no choice...you MUST do it."