It's difficult to say this on here because I know a lot of women whose husbands have cheated/left them find this website a safe space to vent, and there is definite value in that.
However, there has also been some nasty misogynist statements on this thread, so I am now feeling less sympathetic.
It's not always lies that the cheating husband is telling, much as you might want to think it is.
Sometimes he genuinely falls in love with the new woman, and genuinely will treat her differently, because he has genuinely stopped loving his wife, sometimes for "valid" reasons. (Not that anybody needs permission to stop loving someone).
My mom was to OW. She is still married to my dad 50 years later. The love of his life. He had his reasons for falling out of love with his ex. Probably hurtful to her, but there you go.
He and my mom should have waited till he was single before starting the affair, sure.But there you go, everyone doesn't always behave perfectly all the time.
There are loads of similar examples - people still with their affair partners years later, very much in love. You must know people like this - I am amazed if you don't. My own ex husband - still with his affair partner. They seem very happy - they are better suited than he and i were, so good luck to then. Why would I waste my life feeling bitter?
So in answer to the question, sometimes the OW (like my mom, or my ex's new partner) believe the man because he is telling the truth. I'm sorry if that hurts you. Its hurtful nature doesn't make it any less true. Sadly.