You have to think of it as a micro-blog, because that's what it is. Philosophers tweeting their shopping lists, historians tweeting the weekend weather... Why? So they can remind themselves of it, or something else, later.
You're allowed to read it because it's public, but it doesn't mean it has to be useful to you. (Unless you've forgotten to buy milk or bread, or had wanted to go fishing). They're not demanding you read their every tweeted thought, but they're not actively stopping you from it. It's just there to add a bit of colour on your phone, laptop, or ipad.
So you've started following someone because they're consistently tweeting about things that interest you. You find a few of their tweets more interesting than most on your 'feed' (list of tweets that pour in from who you follow. They find that you've retweeted them and may think ah similar interests and choose to follow you.
This is good, now you can tweet privately about your shared interests.
And then you wake up - you've just spent an hour reading, tweeting, re-tweeting, favoriting, and you've completely forgotten to go and get the milk and bread...