This happened a few months ago but the consequences of it keep popping up and I need to know if I'm in the wrong.

I was dating this guy (we'll call him Jack) for about 5 months. We spent a lot of time together, I met a lot of his friends and everything seemed to be going really well. After a couple of months of dating I meant one his friends from his previous school (we'll call her Lucy). Jack and Lucy had been friends since they were 11 and were quite close which I was absolutely fine with until I started to see the way she treated him when we were out together. She would constantly try and be near him, make him laugh, telling him he looked cute "for me". It was so obvious that she was flirting with him.

I tried to talk to him about it but he shrugged it off and said "she's always been like that" which didn't make anything better for me. I tried talking to some of Jack's other friends that I got on quite well with and they all agreed with me that she was definitely flirting with him but none of them had said anything to him. What made it worse is that one of his friends told me that it gets even worse when I'm not around. I trusted him not to do anything and he didn't seem like he wanted to reciprocate it but having someone actively flirting with your boyfriend right in front of you all the time can be very embarrassing.

I tried talking to him about it multiple times but each time he shrugged it off as her being "friendly" and "that's just her personality". I pointed out that his other female friends don't do that, (who I get along perfectly fine with), and he just ignored it. We had a couple of fights over it, one of which in January and after that I decided that I couldn't take it anymore and broke up with him.

AITA? Should I have broken up with him? Or was it just me overreacting to something he was never going to do?