You're going about it all wrong. You think he can be swayed by facts and logic. Clearly that's not the case. He believes in the pay gap because he wants to, not because there is evidence for it. Instead of feeding him facts, accuse him of being smart. He's smart enough to know that women get paid just the same as men. A job opening says $20/hr not $20 for men and $15 for women. So why is he lying? What does he hope do gain? Usually they're trying to sound smart or they're high status parroting the popular opinion that high status people spew. So tell him that his lies are transparent. You know he's lying, and he knows he's lying. No one thinks he's smart, just a lying faggot. He's not popular for repeating what the fake news told him, he's proving he's a brainwashed clown. Insult him and tell him that beliveing what he's told to believe by corrupt politicians and megacorp PR departments makes him an idiot and a fool. Everyone is laughing at him and thinks he's a low status dipshit at best. However that's not enough, you have to tell him that people know this is also a mask. This is the fallback point of the liberal. Oh, I didn't know communism leads to 100 million murders. Bullshit. You know. You're propagating this lie because you're a fucking piece of shit. This will make him want to not believe in liberal lies. Only then will he be open to facts and logic.