According to the ACA in the United States, insurance plans are to cover at least one type of birth control for free. There were some exemptions, like churches. If you are not in the United States, your coverage is likely different. So much of this answer depends upon what it meant by "they".

It is not believable that United States will control the West.

Margaret Sanger was the founder of the birth control movement in the United States and international leader in the field.

The birth control patch fist came out in the early 1990's and has only reached 8% use among the birth control using population. It is however, rising in popularity but is losing ground the internal and hormonal methods of birth control.

Mood swings, headaches, breast tenderness, bloating and breakthrough bleeding are common side effects for women taking birth control pills. Birth control pills were approved for use in the United States in 1960.