“By what moral logic does the state provide one woman with co-pay-free contraceptives while denying the same subvention to another woman when she urgently needs antibiotics for her sick child?”
That’s not even where the contraceptive debate should begin. If you start there, you have already lost. Why should the state compel one person to buy birth control for another person? Make them prove the affirmative case.
Why should the state compel one person to buy anything for another person? Medical care, education, housing, food ... private-pay or private charity.