"What's the harm in giving up my Twitter password?", you might say, "all someone can do is see my direct messages and post a tweet from me, right?"
Think again. The reality today is that social media services are used for far more than just posting updates or photos of cats. They also act as "identity providers" allowing us to easily login to other sites and services.
We've all seen the "Login with Twitter" or "Continue with Facebook" buttons on various sites. Or for Google or LinkedIn. These offer a tremendous convenience. You can rapidly sign into sites without having to remember yet-another-password.
... if you give your passwords to your social media accounts to someone, they could potentially: