Priests should not get married because it would be an affront to their religion and is not in accordance with being a part of the priesthood. Marriage would be a sin for the priest because it would be an outright distraction of their allegiance to the God of their worship.
Not very knowledgeable on the Catholic priest rules and what they can and can not do. However, everything I have read and know about is that the priest are supposed to stay faithful and married to only God, and not anyone else. They devoted their life to giving everything they are to their religion, so I believe it would not comply with the doctrine.