How to use peer-to-peer AirPlay with Apple TV, iOX and iOS Devices
Well, this is actually not a question, it is rather an answer to this problem! I have had this problem where I couldn't mirror or Airplay content from my Mac or iPhone to my AppleTV. It took me sometime but it finally worked!
How to make it work:
1) Forget WiFi network on your iOS / Mac device(s).
2) Forget Wifi Network on Apple Tv
3) Make sure wifi (even if not connected to any network) and bluetooth are turned on in Apple TV and devices
4) Restart Apple TV and devices.
5) You now should find the AirPlay feature on the device. Connect to Apple TV and here you go! Please note that the first time you connect using peer-to-peer it might take several minutes, DO NOT WORRY.
Important Notice: If the AppleTV and the Apple device are both on the same WiFi network, peer-to-peer mirroring will not work, they will use the network to mirror / airplay.
I order for this to work as mentioned above, please check the following:
First, please check that all your devices has the latest software updates.
Second, please make sure that your AppleTV is Gen. 3 model A1469.
Thirdly, check your iOS / Mac device is compatible with this feature, links below
Use AirPlay to see your Mac screen on an HDTV - Apple Support
Get help using AirPlay and AirPlay Mirroring on your iPhone, iPad, or iPod touch - Apple Support
Hope this works for you as it did for me, ENJOY!