He said their conversations are “private”

So I have been in a relationship with my boyfriend for a year now. I am noticing more and more how close he is with other girls. They will call him at 2am and he thinks nothing of it. He will says “ohh I won’t answer it now you’re here”. I always say “no go on answer it in front of me” then he always turns the volume right down so I can’t hear the call. He is constantly snap chatting with these girls. A few weeks ago I saw a snap chat of him posing with the message “you’re hair looks good babe” I instantly flipped. He told me it was his cousin. I nearly broke up with him that night and he literally begged me to believe him. I asked him to show me the messages on his snap chat from these girls. There is one in particular called Hayley who I have never met. She even added me on insta. He said “why are my friends adding you online?” He wouldn’t show me the messages. He said “they are like my boys, and they tell me things that I promised I would never tell anyone else. I wouldn’t break their trust” He turned it as if I was an awful person for telling him I wanted to see. He makes me think I am obsessing over these other girls and that every other girlfriend has been okay with him texting them all the time. Is it me? Am I over reacting? Or do you think something is going on? He is talking about wanting to get married, but how can I marry someone who has these “secret” conversations with other girls. Help!!