aitah for thinking my boyfriend still misses his ex?

i’ve been with my boyfriend for a month, we've been seeing each other since last summer and i am very satisfied with how our relationship looks like but recently we had a fight about his ex. they broke up like three months before we met, same as me with my boyfriend of 2 years. sometimes he talks about his ex, not literally about her, but about how he regrets the way he treated her (broke promises, lied about not using drugs anymore when he did). he also says he isn’t taking anymore now that i asked him not to and i actually believe him. I asked him if he regrets that it didn't work out between them, and at first he couldn't answer me, but he said he wanted to be with me and loved me and no one else matters to him but me. he still keeps in touch with their mutual friend and sometimes he goes out for a cigarette with her. the reason we had a disagreement was because he admitted that the whole time we were seeing each other, he was still asking their mutual friend how his ex-girlfriend was doing. he said he knew it wasn't right and he saw that he shouldn't have done it. every time we see my ex boyfriend somewhere, my bf grabs my hand and shows me a lot of attention, but if a friend he shares with his ex calls or wants to meet him when I'm there, he never answers or doesn't want to go out with her. she doesn't even know that I exist and that he has a girlfriend. I asked him why he doesn't want to tell her, to which he replied that she never asks him if he has someone or how is his life doing. i said that i don’t understand his reasoning and why he can’t even pick up a phone call from their mutuals friend when i’m there and he said that he regrets his contact with that mutual friend got worse and that he doesn’t have a contact with her anymore. the friend and his ex girlfriend have very similar names and at first he said „ i regret having no contact with (ex name) and (friends name). and then he said it was slip of the tongue. should i try to forgive him or is it not the best behaviour from him? i can’t stop thinking about it and actually told him i am thinking about breaking up with him because i think he is not over his ex and maybe he doesn’t even realise it himself.