What could it mean if my boyfriend of 4 years keeps adding his ex to his Facebook?

So when I first met my boyfriend he didn't have her on his profile then a month or so into our relationship I noticed this one girl who kept commenting on his stuff he would like her selfies and all. Come to find out it was his ex. They dated for around two years or so. Apparently she cheated on him and thats why they broke up. He told me the story but not who the girl was that this happened with I found out by his mom accidentally mentioning her name once then put two and two together. I didn't say anything about him having her on there even though I should have cause he lied and said she was just a friend one time... then ended up unfriending her like a year later. Fast forward to a couple months ago I noticed she started commenting on his stuff again and I asked him why he added her back. He was like oh I didn't realize I'll block her... meaning Oh crap I didn't know you knew that was my ex -_- then he confessed to "wanting to rub his success in other people's faces" ok sooo why want to impress your ex?

I told him I dont really care to see her on your stuff anymore. I dont like her bc of what she did and dont think he needs to put himself through crap with her anymore... plus he was away from me on vacation in his hometown where she was when he added her back but swears he didn't see her or hang with her... but I guess the main question is why? Why would a man want to have someone who hurt him as bad as he says back in his life?

Ps I dont keep exes on my profile because I feel like that's in the past. And to show respect for my current relationship.
What could it mean if my boyfriend of 4 years keeps adding his ex to his Facebook?
19
8
Add Opinion