No, it's a good analogy, because it's not between the similarity of people and code. The cases are similar, because in both you restrict freedom to enable freedom.

Making source code available and not requiring the same of those who use it is a temporary fleeting freedom that soon turns into lack of freedom.

Like thinking you're ending slavery by freeing all the current slaves but not making it illegal to own, buy, and sell slaves, or capture previously free people into slavery. Guess if you'd have slavery again very soon?

The analogy is about freedom vs lack thereof, not manual labour vs software. And as you see, it works very well.