Is it selfish to not want your boyfriend to be in contact with his ex?

I really need some help and perspective with a situation with my boyfriend. We have been together for almost 2 years, I thought things were great. But then this year around May or so I was contacted by a female friend of his who tries to make me believe that she was with him for 3 years and they are living together among other things. Basically saying I'm the side chick. He explained that they were involved in the past not while we were together and showed me evidence that she was lying about it and she always wanted them to be together. I believed him and said we would move on. However, since then our relationship has been crumbling. Since I had her contact number I could see her statuses and display pic on whatsapp so I kept it to see if she would show anything relating to him. And I noticed that she did the same because anytime I had us as my display pic she too would post a pic involving him. Most times it was an old photo or had him in the background but she would post it to make it seem like they were hanging out at the time and each time she did he denied being around her. This would happen pretty much every weekend eroding at my trust and our relationship each time. The post that got to me the most was a status she posted with a kitten in her lap sitting on a vaccination card. The card had both their names written on it and her caption said I "mommy and daddy taking our baby to the vet". This time I really lost it and tried to end it but once again we talked and decided to keep it moving. In hindsight I could see she was lying again as I was talking to him at the time of the post so I knew he was not with her. After this I blocked and deleted her from whatsapp. Now on FB she has a post, the only public post on her private set page, a pic with him, her and her parents at her university graduation ceremony. This made me very upset because 1. He did not tell me he was going and 2. Once again she is making a post to create the idea that they are involved or she is significant to him. When I asked him about it he said he only popped in that last 30mins after she asked him to attend and he did not tell me because he knew I would have an issue with it. He also explained that she has been there for him a lot when things were rough for him. I would think that if I were important to him he would understand why him being in contact with her would hurt me since she has been constantly trying to ruin our relationship and he is allowing her to do so by not forming boundaries. He sees where I'm coming from and he says he keeps her at "an arm's length" so he doesn't think that he is allowing anything and that I'm reading to much into everything. He also does not have an issue with the post on FB. Last night,he brought up that he wants a pet to keep him company at his place. I knew that he always wanted a puppy but this time he brought up that he's considering a kitten. He then brings up that she asked him a while back about the same cat she posted and he is considering taking it. This once again upset me and I told him I'd rather if he not took that cat and not contact her since it was used to get between us. He says that I'm being selfish. So with all this being said I would like some impartial perspective. Am I being selfish? Am I overreacting ? Is it too much to ask him to not be in contact with her?

And please google Triangulation. Put it this way: a normal, healthy bloke would cut the (not quite) ex RIGHT out of his life for having tried to put the kaibosh on his romantic relationship! Most with the first occasion, the rest certainly on the second. So why didn't/hasn't he? The answer will come when you google.