Why do so many jobs want employees to keep their income secret?

I had a friend who recently accidentally discovered the payroll records of all of her employees. She was so surprised to find out people were getting paid greatly varying sums to do the exact same job. She also found out some of her subordinates were making more than she did.

I don’t get this at all. I’ve always worked for the public. In schools and libraries, the salaries of the employees has always been up for public record, even though it’s not easy to find. It’s always had a formula. A teacher with this degree and this many years of experience will earn this much money. I assumed that in other jobs everyone was pretty much making the same amount of money for their jobs.

It turns out it isn’t true. Why are salaries so secret in many businesses? I don’t understand this at all. I wouldn’t like to find out that my assistant made more than me.