Guys, My boyfriend is livid with me based off a false accusations. It's our first fight. He wants space. Are there good chances of working things out?

My boyfriend and I are both single parents, and have been dating for over 4 months. We've already established the I love yous, etc. But a few days, I posted something on social media regarding my daughter and her turbulent friendships; and according to him he was accusing me of badmouthing his daughter ( our kids are friends from the same school). Never was it implied or even directed to that child. I tried explaining this, and he wouldn't hear it. The next day, he was still livid for me confronting him, and made it clear to him that it's important to clear up this misunderstanding. He mentioned breaking up because of crossing a line, which I would totally understand when it comes to our kids, but this wasn't the case. He's stubborn and has bipolar, and I'm stubborn with anxiety. After hours of debate and him stonewalling me, he mentioned he'd think about it (working it out) on the condition that I give him space. I asked him how much time needed, and he only said that he'll call or text me when he's ready to talk. I love this man, who has called me his soulmate on more than 2 occasions, and I trust him more than anyone in my whole life. My question is: is he placating me, or is there a chance things can work out after I've given him time?

Guys, My boyfriend is livid with me based off a false accusations. It's our first fight. He wants space. Are there good chances of working things out?
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