Equal and opposite Voltages applied across 2 resistors of equal Value
Rather than "cancel each other out", I would say that the two resistors form a voltage divider between TP2 (-6V) and TP3 (+6V).  

If the two resistors are of equal value, the mid-point must be half way between the two end voltages.  Since the end voltages are equal, but opposite polarity, the mid-point must be zero volts.

This assumes that the amplifier input does not source or sink any current.  If it does source or sink current, the current in the two resistors, and therefore the voltage across them, will be affected by that current, so the mid-point will not be zero volts.