I'm also a Pexer. Having said that, here's my take:
Since this happened only "last night" and you texted the girl this am, I'm assuming the breakup happened only this morning? Who broke up with whom?
In any case, I personally think breaking up is an overreaction. I also agree that you overreacted when you texted the girl.
Honestly, I think you overreacted from the very first moment. Of course, this is just me. But from your story, I deduced that:
1) Your bf did not single out the girl for his invites. You mentioned yourself that he was asking "people" to play badminton. Maybe those people he pmed were from the badminton thread or something so he thought that they would understand his "passion" for badminton. That said, you did not mention if all those people he pmed were girls. So to say that he was flirting, well, I can't say for certain. If he also pmed some boys, would you say that he was flirting with them?
2) You did not say when the exchanges took place, but if it was not even two days, they may not even have met and cemented their plans to go play badminton. Well, from the pm of the girl, it was clear that they did not know each other, so she found it necessary to include her number and info. Likewise, clearly it was devoid of any flirtatious message, otherwise you would have included it in your story. Malas lang niya that she was the only one who replied and so got your ire.
3) Again, did the request of your xbf contain any hint of flirting? Or was it simply straightforward: badminton tayo! Looks like the latter, since you yourself did not mention it in your story.
4) Even the text of the girl that it was okay with her husband shows that she was not even hiding her status, and that her husband may also know of the badminton game. Heck, maybe her husband would also be going for all we know, in case the plans push through. What is clear is that it was clean and out in the open and that she is not hiding from anyone.
5) Finally, you don't even know if his friends are also invited to the game. There was no indication at all that he and the girl are going out alone, right? Considering that he invited a lot of people, maybe that game was meant to be a group affair. Maybe he was right after all, that you were included in the plans, except that there was no definite plan yet.
So I think you jumped the gun here by texting the girl. Maybe he was flirting, but from your story itself, there was no sufficient evidence that he was.
Of course, you also had the right to be upset since your xbf did not tell you that he was planning a badminton game. and that he doesn't play with you even if you invite him. But these are issues that you need to resolve with your xbf alone, without including other people.
