Is writing recommendation letter job for a faculty required?
As stated in the other answer, no professor has to write a recommendation letters for a specific student. The most common reason is that it would be a letter the student wouldn't want anyway, ie a bad recommendation. 

On the other hand, it is part of the job of a professor to write recommendation letters for students in general. So if a professor states that he/she categorically refuses to writes recommendation letters for anyone that would be a reason for complaint to their dean or head of department.