This sentence, “I believe you should never embarrass someone without a constructive purpose.” is not a contradiction to this sentence: “I believe there are situations in which a Beis Din may be required to embarrass someone publicly.”
In fact they are the same thing. If the Beis Din is supposed to embarrass someone in a specific situation, it is because there is a constructive purpose. (which does not mean that it is allowed any time there is a constructive purpose, but in order to be allowed, there must be a constructive purpose.