What would you think if your boyfriend did this?

My boyfriend and I are engaged but just a while ago he let me go through his emails out of curiousity.

There was a girl he dated briefly while back in highschool who had been in contact with him ever since… but it was obvious why she stuck around..

While with his ex, him and this same girl were emailing eachother about when he was dating her. she would say things like “why did you toy me around like that” or “I still have feelings for you” and then say sorry because she had no idea he was having a relationship (even though he was for some time and she spoke to him frequently). They both started saying they missed eachother and she still had feelings for him and he’d go along with it… Emails mostly consist of saying they still had feelings for eachother, how much she still missed him and wanted to meet up with him.

Before when he started having problems with his ex he emailed her a long message about how he loves her, he shouldnt of broken up with her and how much he cared but she said she loved her current boyfriend… but as soon as him and his girlfriend broke up she broke up with her boyfriend… ironic?
Then when he met me she got back with her boyfriend straight away.

When he started a relationship with me he started doing the same thing, emailing eachother behind my back. I was upset because during that time he was already saying to me ‘I feel like i love you’ or ‘I only care about you’ or he’s not speaking to any other girls. The fact he was doing that while with me and saying he loved me made me really uneasy now… I wasn’t sure what to believe… He started to not speak to her anymore because she made me feel uncomfortable and she became vindictive sending me an email telling me off… then later that night sending him a photo of her kissing another girl so… he blocked her from contact and told his best friend to tell her off.

Just know he was sending things like that while telling me how much he loved me and saying so many things to me… I can’t really believe them now after reading those emails… and I don’t know what to think exactly.