I just don't understand how 'allowing' her husband to have sex with other women in favour of staying married to him can bring her happiness.
You are committing the intellectual error of assuming that everyone is like you. She is expressing a desire to forgive him despite his behaviour. She may not be like you.
In fact, I think it's slightly demeaning.
It's only demeaning to someone who wants to be the only woman in the man's life. Some people aren't like you.
It's like saying 'you can still have him, IF you share.'
No-one "has" anyone. You can't "share" a person. Love and attachment are not zero-sum games where if you love more than one person you're somehow cheating them out of what they "deserve". Your language betrays your beliefs about relationships, and your beliefs aren't necessarily true.
That to me is misogynistic.
It's only misogynist if all women are like you and feel as you do. They aren't and don't.
IF (big if) the OP moves through this experience to learn that she doesn't actually care if he's faithful or not, then it would be freeing for her to acknowledge that, not demeaning.
I don't disagree with open relationships where all involved are happy with the arrangement but I don't think it's a helpful solution for someone who's been cheated on for the last 13 years.
I see where you're coming from on this and I don't entirely disagree with you. The dishonesty and cowardice of this man would put me right off him.
But OP seems ok with it. Again, not everyone is like me/you, and my post to the OP was designed to reveal a bit about what her choices might be and what the impact would be. So that she can make a more informed choice, rather than be assaulted with an avalanche of "OMG NO WOMAN SHOULD BE OK WITH THIS!!!" nonsense.
Reducing the avalanche gives OP some space to stop defending herself and dh, and rather just try to carefully, calmly examine her real options.