Bluetooth-Can't pair either iPhone 5 with any Mac-Why?

Subject says it all. All setting in phones and Macs have been triple checked.

Both phones will show as paired momentarily on a Mac (2011 i7 MBP and 2012 mini i7), but just for a second. They then return to unpaired state.

On each iPhone 5, I get a message "request to pair", accept the offer, then get a meesage to the effect that the Mac does not qualify. No pairng takes place.

In system preferences/Network, the Bluetooth DUN is set up, but shows amber dot (not connected). The configuration is exactly as the carrier account shows it, with proper password for that account.

Now I get the message "can't pair because the device is not available.. Connect it to your computer and try again." Well, the iPhone is connected via USB because it needs charging (now at 89%).

I have done everything except restore the iPhones to original state.

Where do I look to solve the pairing problem?