How to resolve Bluetooth pairing issues with MacBook Air and Bluetooth headphones?

"How to resolve Bluetooth pairing issues with MacBook Air and Bluetooth headphones?: MacBook Air won’t pair with Bluetooth headphones"

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Bluetooth AirPhones not Pairing:

Boot in Safe Mode:

Had this issue just the other day. Booting Mac in Safe Mode fixed this. Go here: Start Up your Mac in Safe Mode - Apple Support

Connect a Bluetooth device with your Mac - Apple Support

❝Connect a Bluetooth device

1. Make sure the device (headphone) is turned on and discoverable (see the device’s documentation for details).
2. On your Mac, choose Apple menu  > System Settings, then click Bluetooth  in the sidebar. (You may need to scroll down.)
3. Hold the pointer over the device in the list, then click Connect.
4. If asked, click Accept (or enter a series of numbers, then press Enter).

You can also connect a Bluetooth device to your Mac by clicking  in Control Center and selecting the device.❞

If the headphones in question are older, then they may not be compatible with the Bluetooth version of your MacBook Air.