Why is only one out of 2 batteries is discharging when connected in series?
Voltage is not a reliable indicator of charge state. 

Both batteries can have a terminal voltage of 12V, but one be half charged and the other nearly dead.  Running them in series will work until the weakest one is completely discharged.  

At that point, the battery that still has charge begins pushing current through the discharged one.  This "charge current" is running in the opposite direction from the current when the battery is being normally charged.  Sort of like if you connected a 12V battery charger to a battery backwards.

This "backwards charging" will usually destroy the battery.  This has happened to your battery.  A discharged battery will usually show some voltage.  Yours is showing 0V, so it is shot.