What would be the real-world equivalent of handing over your social media credentials to your employer? Would it be like handing over your house keys? Or more like letting your boss read your journal?
Whatever the analogy, the point is that social media accounts feel personal to the user.
Even for those who broadcast loudly about themselves in public, there are parts of social media that are inherently private, and employers know this. So some are going so far as to ask employees, both existing and potential, to hand over social media account information so they can have full access to everything in those accounts. This includes personal messages, which are never made public, as well as posts that are shared with select groups of people, not the general web.
For companies contemplating such a policy, beware: Legislators are already taking steps to prevent it. And, according to the user terms of service for Facebook, Twitter and LinkedIn, sharing login information is a no-no.