1. Sex, when not done specifically for procreation, is a recreational activity. If you are trying to procreate then you don't need birth control in the first place.
2. Since birth control is only needed when not procreating, it is only used for a recreational activity.
3. Birth control is therefore an accessory for a recreational activity. Much like a bat for baseball, a backpack for hiking, or a Kinect for the Xbox.
4. Recreational sex, while enjoyable and having some health benefits, is not necessary. You will not die without it and many of the health benefits it provides can be receive by other means. mountain biking, hiking, sports, even video games (in moderation) have health benefits as well.
5. Therefore birth control is also not necessary as it is only used to facilitate recreational sex without procreation.
6. There is no good reason why anyone should be forced to pay for it for someone else, unless you also advocate insurance covering my next Xbox, mountain bike, etc.