garage light with two hots and one neutral
It's not a live wire at all.  It's a neutral.  This part of the circuit doesn't just serve the light.  It also carries power (hot and neutral) onward to other loads.  

The always-hot is carried from wherever (switch, perhaps?) on the black wires tucked in the back there.  

The switched-hot is carried on the red wire, obviously you want the lamp to take its hot from the switch, so it isn't on 24x7. 

The neutral wires brought 


Neutral from supply
Neutral onward to other points of use
Neutral to the lamp


You only connected neutral from supply to the lamp, so neutral was severed to the  onward points. 

Electrical current flows in loops.  Power is going out the hot wire to those onward points of use, but then is unable to return via the neutral you severed. 

You see "hot" because electrons are queued up there waiting to return via neutral. This is normal when a neutral is disconnected; it's one reason neutrals need to be treated as hot wires from a safety POV.