Why it worth to read generic management literature

Actually not, if you are completely satisfied with your current position and don't want||plan to change anything in future.

If your case is different, then there are at least several reason to read a few management books or take special courses:

1. There are some things that are being taught everyone, who ever takes management courses. Among those basic knowledges, there are some items that look quite interesting and thus are easy to remember. People do remember those items and start referring to those statements in their business or even personal life (at least for some time after learning the topic :-)). It usually worths to know what are they talking about to understand them or to argue. You don't have to take this information too serious, but it still makes sense to get it. Among such basic staff, I can mention:
• Maslow's hierarchy of needs (or just Abraham Maslow pyramid);
• Urgency / Importance quadrant by Stephen R. Covey. BTW, there are also some more popular things introduced by Covey, so I would recommend to read one of his books;
• Conscious Competence Learning Model.
  
  
2. Sometimes such reading is fun:
• Peopleware. Productive Projects and Teams. Tom DeMarco & Timothy Lister;
• Screw It, Let's Do It by Richard Branson;
• Slack: Getting Past Burnout, Busywork, and the Myth of Total Efficiency by Tom DeMarco;
• Life Inside a Bubble by Igor Ashmanov (the book is in Russian).
  
  
3. One more interesting category is "courses/manuals" for top managers. A lot of them are too obvious, some advices are really stupid, but anyway it worth to read to understand your bosses :-) Really, when you read this kind of literature, and find a lot of recommendations your boss follows or better has just recently started to follow, there is quite high probability that she/he will follow other instructions from the same source. I won't provide exact references in this article to avoid unnecessary rumors in the companies that I was working with. However, the rule does really work!
   

Disclaimer: if you are a technical specialist and believe that it's your right way, don't spend to much time on managerial staff. Few books on this topic is more than enough to get an idea what is this all about. Keep your valuable time for more important things, keep going through IT news, learning new technologies and increasing your professional skills.