apple tv stuck on ethernet no option for wifi

It is possible your Apple TV is out of Wi-Fi range. There are a couple of things you can attempt.

Please do the following:

1. Unplug your modem from its power source for 2-3 minutes and please restart modem.
2. Unplug your router from its power source for 2-3 minutes and restart router.
3. Unplug Apple TV from Power for 2-3 minutes – re-plug in and retest. 

If the above steps do not work, then you may have an issue with your network providing an adequate Wi-Fi signal where the Apple TV is locate in your home. Please use a tool such as iStumbler to check the Wi-Fi strength.

If you still have a problem, you may have some additional security setup on your network that is preventing the Apple TV from receiving a WiFi signal.

Please unplug your Apple TV from it's power source for 2-3 minutes, then re-plug it in and re-try.

I can't help if you don't want to follow the recommendations.

Good luck.

Good luck.