Cannot disable Find My iPhone

Hello. I need to turn off Find My iPhone, but when I try I get this message:

Verification Failed

There was an error connecting to the Apple ID server.

I followed the directions put out by Apple Support. The directions said that for this problem, go to iCloud.com and remove your device from Find My iPhone. I did this and my device was successfully removed; however, in my actual device settings, Find My iPhone is still turned on and the same massage keeps coming up when I enter my apple ID. How can I fix this?

Note: my phone is unable to connect to Wifi