First, let me say something that people might find useful. I go to display perferences, there is an "Airplay Display" drop down I can use to turn on mirroring. I have NO TROUBLE enabling airplay mirroring from there even though the icon is missing on my menu bar. It's a pain becuase it adds several steps, but it works.
Now, unto a complaint about this thread...
I am really annoyed by the people here re-iterating over and over again that this is due to people having old hardware. I read the requirements and my Macbook meets them. What people are missing is a shortcut that used to be in the menu bar that is now gone. It is missing for me was even though I can get Airplay mirroring to work. It appears when I turn mirrioring on, but goes away once I turn it off. I used to always be there.
Drop the constant reminders of hardware limits. The fact is, even if you meet the requirements, this is an issue. I am sure not everyone is experiecing it, but the icon is gone for me and it should be there.