"Busyness" is a social defense against other people making us do things we don't really want to do and a mechanism for coping with feeling guilty about things we know we should do, but don't. My intuition is that people have had to project themselves as busier and busier over the last couple decades as technology has made us more efficient in order for this strategy to continue working.
If you're always "so busy!", your boss is less likely to give you more work; your spouse is less likely to ask you to do more around the house; you're not going to feel as guilty about only seeing grandma once a year or refusing to help your friend move; you can feel a little better about yourself when a friend lands an awesome new job or plans a cool vacation and you haven't really done anything. When you haven't seen someone in a long time and they ask how things are, you can give them the impression that things must be even better than the last time you saw them, because you've clearly been so busy improving your lot in life. Well, that's the idea, at least.
After I read that article I decided to try to be more honest with myself and the people I know about how busy I really was (which is often "not very" - I, like the author, am the "laziest ambitious person I know."). It's a very hard habit to break, and it forces you to be more honest about the things you really want to spend your time on and the things you're avoiding.