Just wanted to say I was having same problem doing a second pairing for my Jaybird Sports headset. Worked fine with iPhone 10.0.2 but it did not show up as a choice in the BT menu of my MBA 10.12. So I tried this and it worked:
1. Went to iPhone BT menu and selected "forget this device"
2. Turned off iPhone BT
3. Went to MBA BT menu, held down Jaybird POWER ON button and the MBA BT Menu displayed the Jaybird as an option to pair.
4. Went to MBA BT menu and selected option to disconnect the Jaybird, then powered off the Jaybird.
5. Turned of BT on MBA
6. Turned BT on in the iPhone settings and held the POWER ON button on the Jaybird
7. The iPhone displayed the option to select the Jaybird for pairing and was successful.
I do not know why the Jaybird did show up as an option to pair to the MBA after I first paired the Jaybird to my iPhone but it did work in the reverse. So for others, first try to pair it with the MBA and then try to pair it with the iPhone.
All the best from another retired USAF Flight Nurse.