You are not speaking to Apple on these forums, we are end users like you. Sorry you felt reprimanded however we cannot help you unless we have some context. Did you follow the steps in the link that I provided earlier. If you did and you are still having an issue then please do the following:
An AppleTV 3 is a VERY VERY old device now, close to 10 years old. You may want to consider upgrading it to an AppleTV 4K, you can find them on Apple's Refurbished store for about $109.00. However where I would start is by doing some basics:
- Unplug your modem from power for 2-3 minutes and then re-plug it in. (yes even if everything else is okay.)
- Unplug your router from power for 2-3 minutes and then re-plug it in.
- Unplug your Apple TV 3 from power for 2-3 minutes and then re-plug it in and then test to see if AirPlay is working.
Also, if you have a home fits any of the parameters below you may be a candidate for upgrading your home's network:
- 1500 square feet in size or larger
- 2 or more stories
- Supports more than 7-8 Wi-Fi devices
- You occasionally lose Wi-Fi signal in the home with other devices (iPads, iPhones, tablets, etc...)
- Current router is 5 years old or older.