I know a few people like this. Turn their noses up at facebook (fine, their choice) but then go "wah, why wasn't I invited" when people make plans using facebook groups.
Case in point there's a fb group for parents of DC in my DDs year. People use it for things like reminders about what homework/spellings are this week.
Also sometimes gets used for social things - e.g. " a group of us are going to X play centre after school tonight if anyone fancies it."
I like fb groups for organising group activities - it's massively complicated trying to arrange things like that via text when you can't see what others are saying, email is too complicated as you end up with a gazillion emails and many of them cross.
With a fb group you can have a group conversation, it just makes sense.
But some people can't possibly just join fb to join a group and then just not indulge in the bits they don't like, they're too good for that. Fine. But don't then go '"WAH! I got left out!"