Up until recently, it wasn't guaranteed to be covered under your health insurance. The ACA — "Obamacare" — required plans to cover many options, but it's not guaranteed that your preferred option(s) will available. Generally, coverage is supposed to be free, but again, only certain options may be free (generics only, for example) and some may require a significant copay (IUDs, I believe).

For the birth control pill, you still A. need a prescription (which usually means you need to occasionally make an appointment, take off work, and see a doctor, probably not for free), and B. need that prescription to be filled. Oftentimes, that means picking up a new package of pills in a five-day window during semi-limited business hours because many pharmacies avoid giving out an extra supply. Planning for a vacation can be a pain (1-month notice) but an emergency trip is almost undoable.

Not every pharmacy even needs to carry the birth control pill or other options, so it's a very real scenario that people may not have access to their preferred method. Recent court challenges (Hobby Lobby in particular) have made it more complicated and allowed some companies to NOT provide such coverage.

Also, pharmacies have not been above charging women for products that should be free.

Lots more detailed info here: http://obamacarefacts.com/obamacare-birth-control/

IANAW but I am married to one.