The idea is that the first person to give a number loses, since that anchors the conversation. As an employee, it's an counter to the asymmetry of information. Employers know their own salary structure, and even have access to anonymized salary survey information. Employees don't have this information.

Conversely, encouraging employees to not talk about your salary to other employees is another tactic to keep the information asymmetry. If you're underpaid, you'll never know it, and that's how they like it.