See jobs by hovering over name.

If someone has a job they have a colour that go with it and is universal and seen on either the Job List or Marauder's Map. So you basically already know if someone's a teacher of a librarian etc.

I think what they are trying to say is it would say the specifics of the job. If you see a teacher in chat, yes, you know that they are a teacher, but you do not know what they teach. Same thing with management and assistant teachers. 

Sure, they can look at the user's profile or the job list, but it would be quicker if it were added to the hover profile and would help users who are fainted. 

but the colour already tells you what he is, and only for teachers, AT it differs what subject they teach but they are still teachers. and for management you have the same but most of the time (if you are active around the site) you will get to know who teaches what so i think this would be rather pointless

You can't assume that all users are active or already know all of the staff members well. What about new users? They join every day, and I know from experience that it takes at least a few weeks to learn who teaches what and who is management for what, and that takes time going back and forth from the job list.

Just because you want to think "Well, if they want to know who teaches what, they should just be more active," because sometimes people are busy, sometimes they need a break, sometimes they are genuinely new to the site. It wouldn't exactly be fair to think that way.