From my perspective, the best parts of being a supervisor are the parts that do not involve having to discipline people, to scold them, or to otherwise make them unhappy. Those aspects of the job are not pleasant in any way.
One of the major duties of a supervisor is to act as a coach to employees. A supervisor should help employees learn their jobs. The supervisor should train them and show them better ways to get work done. This sort of thing is enjoyable in most cases because it involves doing things that employees will generally appreciate. Work is always most enjoyable when it is appreciated.
Another major duty of a supervisor is to make plans and analyze operations. This, too, is an aspect that I enjoy. I like to look at the workings of an organization and try to figure out what could be done better. I like to try to determine if there are things that are not being done in optimal ways.
These are my favorite supervisory duties because they are the ones that allow me to think and to interact in positive ways with the people who work for me.