Messy breakups

So my boyfriend and I recently broke up...we agreed it was best to be just friends. It was hard at first, but I made peace with it because I believed it was what's best for him because I truly loved him, and just wanted him to be happy. We got along very well. We shared similar values, and overall it was a very special relationship. I missed him a lot a few weeks after the break up, and would text him from time to time. I would start the conversations and he would always end them by not replying. I started feeling unwelcome and felt like a bother. I was confused because I had thought we were friends. But now, he's just ignoring me. Now, when he initiates conversations, I don't bother to reply because what's the point? The conversation will end anyways. An issue in our relationship was how he would act on social media. I found some of his actions disrespectful, and I told him about it. He said he would change, but he didn't. And now, I see him talking to this girl who he tried to go for before me. Any advice?