Why can't my heart and my brain work together on this?
I think they are. You might not like what they're saying, but I think they are.
Your heart is telling you that this isn't right for you. And by "this", I don't mean polyamory necessarily, but
this "polyamory" that is being pitched to you in
this disrespectful, shitty, insensitive manner.
You
should feel angry. You
should be upset. Someone who is supposed to love and take care of you is trying to sell you on an incredibly shitty situation (for you), and make you love and enjoy it and want it. He's trying to guilt trip you. It sounds like the most he's admitted of his own problems in this situation is to say that he's acting "a little bit selfish".
Do you realize that he's trying to gaslight you? It sounds, from what you've said, that he's either been incredibly unhappy for years and hiding it, OR (maybe) wasn't, but now there is this
thing he wants (and it does sound like he's treating this other woman like a shiny new thing than a person), and what better way to get it quickly and without any chances/concessions towards you than to say that he's been "incredibly unhappy" for years and that you "owe" him?
Has he said what he's incredibly unhappy about for years? Because really, with all the other lying going on, I'm tempted to call shenanigans.
Also, unless he's been incredibly unhappy not having a girlfriend for years, what the hell does adding a girlfriend do to his unhappiness? If he way say, unhappy because he had all the stress of being the primary breadwinner in the house, the solution isn't a girlfriend. It's maybe you getting part-time job, or him getting a different job that pays better or maybe you getting a full-time job while he stays home with the kids a few years or something that is at least
related to what he's been unhappy about for years.
That's assuming this unhappiness is really a real, years-long issue. And if he hasn't said exactly what he's unhappy about, I would really be concerned. People who have been unhappy about a particular thing for years can usually go on about it for hours at the drop of a hat.
Anyways, whether or not he has been unhappy for years, the universe does not hand out consolation-prize girlfriends to assauge said unhappiness.
And I think your heart and mind are working wonderfully. They're also giving you a lot of pain, but that pain is better than the death-by-degrees you'd suffer if you allowed him to talk you into this bullshit triad.