If that's the case, if healthcare is going to be cheaper, then why is it a crime not to be a part of the system? It just doesn't make sense to me. I can't understand why it would be illegal to financially distance yourself from something.
The wording of the law as a ''crime'' is to increase coverage. You're missing the point. The government doesn't care about minuscule control, it doesn't care if individuals choose not to get healthcare, and hence because of such poor foresight, by chance die in the future due to bad choices. It can't give two hoots about interfering in your little life.
It cares about the consequences of these actions on society as a whole. Healthcare is a good with positive externalities that we are not always aware of, or at the very least do not care about. When humans make economic choices, we most likely only take into account private costs/benefits. I.e private marginal costs and private marginal benefits. We do not take into account what society stands to lose or gain. Healthcare does provide benefits for the individual, but it helps society. People are less afflicted with illness, worker productivity goes up, less subsidies are needed to cover their treatment in society, etc etc.
We underconsume healthcare, just like we underconsume almost all goods with positive externalities. This leads to a deadweight loss, a loss in welfare to society as a whole as seen in the diagram below.

There is a divergence between MPC and MSB (Social Marginal Benefit) if we follow market forces solely, which ends up at the equilibrium quantity of Qmkt. The red triangle represents the deadweight loss; ideally to maximise efficiency and benefit, quantity consumed should be at Qaff, at point M. Making healthcare compulsory pushes this up, and society as a whole benefits.
If I hold a gun to you face and buy medicine for your illness, you should be allowed to sue me and I should be imprisoned. It may be beneficial to humanity to force them into good health, but coercion is not the answer.
You're exaggerating it. It's just a penalty to companies.
To coerce others into buying healthcare is a statement that you know better than everyone else, therefore you should have the power to tell everyone else what to do. Let people make their own decisions and use education and other means to help others.
Education has a long gestation period, or doesn't work. Environmental education has been here for years, yet people still leave such huge carbon footprints, refuse to recycle, and the lot.
There are starving children in Africa, am I justified in stealing money to provide food to those children? No, I am not. Why should it be any different for healthcare?
This isn't even a valid comparison/analogy. There's hardly a link here. Obamacare is not ''stealing'' money to fund itself; it is raising taxes through a variety of ways, such as taxing those corrupt insurance companies.