Is it a social faux pas to not have coworkers on facebook?

[*Expat Jane*]

I remember reading article a while back and it was talking about how it is a good thing to have coworkers on your facebook page etc. I work in a library and people at work show me their FB page and they have other coworkers on it. I believe in separating my work and social life and someone made a comment to me how I was too private. Is it wrong to NOT have coworkers on your page? I see myself as friendly but not friends with the people I work with.

I have trust issues with them bc although they act like friends and have each other on their pages they are quick to talk negative about others if the friends is absent from work

[Nunya]

Facebook is for non-work friends and family. No one else.