"It doesn't matter where they've come from or how much they've earned in the past."
Nonsense. Come from Oxbridge or RADA or an impressive company then you're in a better position to be paid more as you're likely a better employee.
"If they are doing the same job they get the same money."
Yes, but as jobs and responsibilities get more complicated, so does the ability to compare them.
"The public sector makes it easier to pay equally because it has set pay scales"
Yes. And the public sector is fucked. Wasteful and, well, fucked. Full of tossers earning more than they should be because they have incremental pay rises for time worked when half of them should be kicked out on their arse.
"But isn't this ALWAYS how men get paid more"
Except it isn't.
On the lower rungs of graduate employment, women earn more than men. They're more likely to have a better job and more likely to get promotions.
Then something happens around the age of 30. Women ... ah, can't for the life of me remember the reason for so many women no pursuing their careers less vehemently after this kind of age ...