The reactionary argument that providing birth control to women in order to increase their personal autonomy will lead to more sluttiness which is a bad in and of itself. Once we strip out the patriarchial authoritarianism it sounds like a Jevon’s paradox argument:
improved efficiency lowers the relative cost of using a resource, which tends to increase the quantity of the resource demanded, potentially counteracting any savings from increased efficiency
Properly used birth control lowers the potential costs of any given sex act by at least reducing pregnancy risk if not also disease risk. Therefore, more people will have more sex,(why is that a bad thing?) and this increase in sexual incidents will lead to the same number or more of pregnancies, STDs or sexually empowered women.
That is the argument.
We observed a statistically significant decrease in the fraction of women and adolescents who reported more than one sexual partner during the past 30 days from baseline to 12 months (5.2% to 3.3%; P<.01). Most participants (70-71%) reported no change in their number of sexual partners at 6 and 12 months, whereas 13% reported a decrease and 16% reported an increase (P<.01). More than 80% of participants who reported an increase in the number of partners experienced an increase from zero to one partner. Frequency of intercourse increased during the past 30 days from baseline (median, 4) to 6 and 12 months (median, 6; P<.01). However, greater coital frequency did not result in greater sexually transmitted infection incidence at 12 months.
The cost of sex is an amazingly complex multi-variate problem with health, emotional, social bonding, and physical interactions.
Let’s take a leap for a moment. The IRS currently gives a standard $0,56 a mile deduction for business use of a car. That $0.56 is the sum of a variety of costs. Fuel is calculated on the assumption of an automobile gets roughly 25 miles per gallon and it tends to be about $.13 or $.14 cents per mile. Most of the remaining deductible allowance is built on depreciation, insurance and repair costs. Personal time lost in traffic is not included in this calculation.
The argument that a rapid conversion of the US automobile fleet from pure internal combustion engines to hybrids has produced some really bad arguments at the usual places that this won’t do much if anything for US fuel consumption as efficiency gains will be consumed by increased driving (let’s not look at the secular trend of fewer vehicle miles driven for the moment as the theory does not predict that).
The problem is that the true cost of driving between is the cost of the car plus the cost of time in a car. A low estimate is a dollar per mile. Doubling fuel efficiency decreases the cost of driving by perhaps 5%. All else being equal, people may be slightly more willing to drive as it got cheaper, but a new equilibrium of more cars on the road leading to more congestion will quickly increase the time cost of driving the same mile.
So back to birth control, it reduces a particular set of costs (pregnancy and disease risk,) as well as increasing the option value of having sex for a woman on her own terms. However, these costs are often dominated by other interwoven factors, so the birth control leads to women having too much sex (if you can even assume that is a problem) argument fails on its own merits.