why does higher current mean lower discharge capacity
Yes, twice the current discharge means half the time to battery depletion in the ideal case.
The capacity (at least to a first order) is  the same in both cases.
A battery's capacity is the energy stored, measured in amp hours, ergs, joules, or whatever unit you like.
Watts are volts*amps or in your cases battery voltage times 1A, or battery voltage * 2A.  So twice the power for half the time is the same amount of energy drained from your battery.
EDIT: If the question is why would the battery capacity decrease over the expected ideal, then Brian's comment is the answer.  The internal battery impedance means more power dissipation at higher currents.  The chemical reactions in the cell are non-ideal as well and become less efficient at higher discharge rates.