Maybe you like birth control and you think everyone should have free access to it. Fine. The HHS mandate at it's core is not about that. It's about religious freedom, the freedom to follow God's laws and not be forced to break them because your government made another law.
If you're an American, you ought to have learned that America was founded on religious freedom. So many of the original settlers fled Europe to escape persecution and to be able to practice their faith freely. Many were Catholics, but many more were Protestants. Freedom of Relgion is one of the primary reasons that America is the great country it is today.
If the HHS mandate is not overturned, we will lose so much more than schools and hospitals. So much more.