Q: Your software is up to date ! I need to update to iOS 10

Be SURE that you have an iPad (4th Generation)
Identify your iPad model - Apple Support

Ultimate *i*Lookup is consolidated into > http://www.everymac.com/ultimate-mac-lookup/

Does your iPad have a lightning or long 30 pin dock connection?

Also, in Settings app under the General panel, tap the about this device/iPad and provide us with the model number.

The model number starts with an M.

Thank You.

It could be a misdetection if you're absolutely sure your device is 4th gen. A simple turn off and back on can sometimes fix iOS detection. There was discussion a few days ago about an iPad 2 (not Mini 2) detecting iOS 10 update. That should not have happened. The user restarted the device and it detected iOS 9.3.5.