Why does my bf ping pong between his ex and i?

My boyfriend left a girl he was dating to be with me. He told me how he complained to her about standing up to her family,stop letting them control her,and she never did it and how her family didn’t even like him to begin with. He said his pet peeve was her not driving long over/not spending the night all because of her parents.So the last day of February he left her and ten days later we were in a relationship. He bluntly told her he met someone else and was leaving her. Today i went through his phone.The day after he broke up with her though he texted her first saying “hey sweetie how are you doing” he initiated the conversation the next day after that too saying “hey sweetie how’s your day going so far” the week after he broke up with her she was still trying to see him and he was trying to clear his schedule to see her too from the text. Two weeks went by and neither one of them texted each other until last Saturday he texted her first asking how she was doing she didn’t reply. Then today i see text from her saying she missed him and said she hoped he was doing good and he said i miss you too sweetie i hope you’re doing alright sweetie. I see text from both of them bringing up old memories and bringing up their inside jokes as well ... but he left her to be with me