It's all in the words.
Being an authority figure means that you must have standards of being firm but fair. Always holding the attitude of being a teacher and instructor.
Being critical and judmental is the attitude one takes toward others often times while in the role of authority figure. It is the attitude of one pulling another down to elevate their position. It is more than likely a person with significantly low self esteem that must shame and minimize others in order to fulfill their own need for elevation and acceptance