Obamacare and the Freedoms

In reading about challenges to Obamacare on First Amendment grounds, I am puzzled. The challenges are all about religious freedom. I think that's wrong. The First Amendment also is supposed to guarantee free assembly, and I think that's a better argument. It's also my major complaint about socialism in general and Obamacare in specific.
 
Free assembly means you have the right to choose your associations, be they personal or business. The Obama government is forcing you to make an association, one with an insurance company which you may not want, which in my view is clearly unconstitutional. Unless you're a lefty.
 
If you agree with me, feel free to forward this. I think maybe we need to show the lawyers - who seem immersed in the minutiae of law - how to get back our freedoms.