Broke it off with guy I really liked as he was messaging other girls

I don’t know if I’m over reacting, but I was seeing a guy for just over a month, went on a few great dates, stayed over at his multiple times, had great chemistry (physical and emotionally too) however I found out last week that he is texting other girls even though when we first started dating we agreed we wouldn’t be seeing other people. I stopped speaking to other men who tried to pursue me and I was really enjoying the way things were going and wasn’t ready myself 100% for a relationship, but in all honesty I could see myself with this person long term. Tonight I went round to his to collect my things and I explained that I wasn’t happy about seeing a text from another girl, he admitted that he was still messaging other girls but wasn’t physically dating anyone. I told him that I wanted someone who was only interested in me, that I wasn’t an option and that I don’t want to be one of many and he told me he respects that but he isn’t fully ready to commit to anyone and he’s happy having no pressure. He said he thought I was amazing and that he would be there for me if I ever needed to talk. I can’t help but think maybe I have over reacted to the situation and should be unbothered that he is messaging other girls however I also cant just accept this behaviour from somebody and personally I feel that if he thought I was so amazing, cutting these other girls out of his life wouldn’t be an issues? Please any opinions would help in what I should do