Perhaps someone can explain this to me

Let's start with this:
http://factcheck.org/2010/03/a-final-weekend-of-whoppers/

I'm glad to see a low-bias, honest presentation of the facts. One fact, though, that I don't see emphasized enough (here and in a lot of other places) is this: "mandating that individuals buy coverage". Why is this okay? Why would this not be seen as an outrageous affront to my personal liberty?

I've heard that if one does not accept the mandate, one must pay a fine, a non-insurance fee. The rest of this rant is based on the quite possibly false assumption that this is true.

Consider this. Let's say I give you the following choice: either you
1- chop off one of your feet and I give you a magical golden blanket that keeps you from getting sick (maybe); or
2- chop off one of your toes. You get nothing in return and your toe goes into a pot to help pay for other people's magical golden blankets.

Now, nevermind which option you choose- you can decide on your own time and keep that to yourself. What I want to know is:
Is it a good thing that you are being forced to make this choice? Hypothetically, am I a good person for forcing this choice upon you?

I'm sure I'm missing something here and I'd greatly appreciate someone telling me what it is, please. I'm honestly curious. If I'm not missing something, then I'm just baffled.