There is more than one way to answer this question. Nancy has given you a philosophical answer, and Karin a pragmatic one. I would agree with both. If you want to understand the specific topics and information a person must have to be a group exercise professional there is no better way than to read the manual for one of the major national certifying organizations. I own and have used the ACE manual and agree it would answer your questions specifically and thoroughly. And Nancy is correct that the way that information is understood and applied varies with each fitness professional. Our clients/students are each unique, and each of us must be flexible in the way we meet those needs.
Also, keep in mind that there are different sorts of fitness professionals, and the requirements differ for those different areas. For example, although there are some training programs that allow one to work in limited ways with nutritional information, to work fully in that area as a nutritionist requires a degree and licensure. Someone who works with the martial arts requires training within that specific field.
I don’t think we can answer you more fully as to answer the question you pose is to ask both for a full instructor manual (which you can get much better by buying something like the ACE manual) and a meditation on our life work.