Fine that it didn't work out as he thought and he called an early halt, not fine that he got in a massive strop about it with you.
This. It sounds like you had discussed how you thought it might go before it happened, but hadn't really discussed how to handle it if either of you didn't find it going as you were comfortable with or had hoped it would go. There are always unknowns in threesomes - lack of chemistry, nerves, fantasy being better than reality. My last one - unexpected period, which was somewhat limiting.
I've been swinging and had threesomes. If you're going as a couple, it's important to trust each other and communicate with each other. It was bad form for your woman to carry on with you and push him off, but people don't always behave perfectly, especially if caught up in the moment. You should have probably involved him more - he could have gone behind you and been touching you, even if he wasn't touching her. But it was your first time, and you can't always predict how you will feel. It also sounds like she was up for more than she really was - that can happen. Sometimes you meet people face-to-face (be it a date with a single person or a couple,) and realise that in person, just... no. He still had no right to get stroppy about it, especially as he had said he'd like to watch you - he should have calmly discussed feeling left out afterwards, and how to handle it better in future.
I have always been careful to make sure no one is getting left out. I do usually leave arrangements to my partner (out of laziness, tbh,) but we do now discuss who he's chatting to before agreeing any meeting, because someone just being available isn't enough for me to fancy them. If you're meeting a couple, this can be even trickier - the men are often not as good as the women.
I've done MMF at clubs where I'm the centre of attention, but only FFM when specifically arranging a threesome. I've had a few men (more than I would have expected,) asking for MMF, as they're bi-curious - I've always said no to this. I'm not interested in watching two men get it on together and leaving me on the side, and I think it would be too big a risk, and though I hope they find people to explore with, I'm not setting up as a matchmaker, either.
I have a male friend whose marriage broke up, because his wife went off with the woman they met. I've met couples where it works well, they're tuned in together and check in together often. I think communication is key to any relationship, but even more so if you involve others. Getting in a strop is no part of this, and I'd be put right off. (I would be put off by tantrums over pretty much anything, sex or housework or otherwise - I tend to respond better to reasoned discussion about disagreements.) I need to have trust that they'll deal with disagreement in an adult way, more than I worry about jealousy.
I think you're right to sort things out with him before meeting with her again.