A man’s work is not a personal matter, it’s a social matter. There’s no such thing as a personal matter—or a personal life. That’s what we’ve got to force them to learn.During a discussion, a character makes this point in an argument for passing an extremely socialistic law. On its face, it seems to be about work being a public "matter," not a private one, but it's important to work backwards to understood its roots.
Fundamentally, the quote is about who your life belongs to, you or everyone else. When it says that work is social, or public matter, it is saying your life belongs to everyone else
Now take the word social and consider how we typically use it. What types of people are more social? They know more people. They go to parties more. They have a "good time." Their lives are very public (in the circles they run in). Everyone knows what they do and who they do it with it. In other words, their lives, essentially, belong to everyone else.
Now consider that we say that those people are the ones who have personal lives. Except, we can now see the inherent contradiction in that idea. By being "social," as we've come to understand it, their lives are necessarily not personal. A personal life is a life that belongs to only you.
I'm not suggesting that having a social life is bad. Rather, it's important to consider what a true social life is, and where (if) that diverges from your personal life. Think about what I've written here and observe the most "social" people you know. You'll probably discover that they have the least personality of anyone you know (because they generally reflect/emulate the people with whom they are currently being "social.")