but I really believed he was trapped and she was selfish and cold
Sadly this is little comfort for the wife who in all likelihood was none of those things.
Maybe she was, maybe she wasn't. That sort of thing is very much in the eye of the beholder and marriages are complicated - no two are ever exactly the same and not all adulterers are blatantly lying about their spouse in order to get sex. Clearly some genuinely feel that it's the truth.
I have a friend who was recently devastated to find out that her DH had been using hook up sites. It has taken months of semi-separation (at her insistence) for her to finally decide that she won't have him back. All this time he's been waiting with his tail between his legs like a scolded puppy, jumping when she says jump, then being sent back to the doghouse for a few weeks. He has promised everything - they'd move house, he'd leave his job and start afresh somewhere else. He'd work from home so he'd never need to be out of her sight again etc.
Whatever she wanted he would do - just please don't leave because he loved her, he'd just been weak and stupid because he craved sex and physical affection.
Anyway, she's now told him she can't ever move on from it, so that's that.
The thing is, all us women who knew them well as a couple have been super supportive of her and very critical of him for obvious reasons. But since she's announced it's over, I've had three separate female friends quietly say to me that actually, she was always cold and selfish towards him. She never showed him any affection or said anything nice or encouraging or supportive to him and she would openly tell everyone that they never had sex any more in a loud jokey way but it was humiliating for him, because it was her choice, not his.
One by one all our mutual friends have admitted in hushed tones that looking back, there didn't seem like there was much affection or respect on her part. She was often quite dismissive and disdainful and would criticise him in front of his friends, and make jokes at his expense. And he was always nothing but a gentleman to her, as far as we could tell. 
My DH has commented several times in the past 'why is Sue always so horrible to John? If you spoke to me like that in front of our friends I'd be furious.'
So when someone tells you their sex life is non existent and their partner is cold and distant and they are lonely, it's not always a lie.
And to his credit, he has never ONCE said anything negative or critical about her during all of this and has never ONCE tried to excuse his behaviour or shift the blame onto anyone but himself. He holds his hands up fully to being in the wrong and he's lost everything because of it. He'd go home tomorrow but she won't have him.
So maybe OP, this is what you are dealing with. Yes his wife is not perfect, she might be cold and selfish at times but he loves her and his kids and his life with them more than he loves you.