It's really very simple. It's cheaper for insurance companies to provide birth control than it is to not provide birth control.
Let's take all the insurance companies out. You are newly married. You will pay ALL your family's medical expenses out of pocket. Over the next 50 years, would it be cheaper for you to pay for birth control and have two kids, or not pay for birth control and have 12 kids?
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“Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it.†– Richard Feynman