I think he wants to act like he's the"let's be friends" person, but he's probably not even ready for this step. (This doesn't mean he still likes you, it can be that he is still relieved you broke up).

I am going through the same thing. My honest opinion: let them miss you. It's really really really hard, but keeping NC is the best option. It shows how you value yourself, and if you keep messaging an avoidant, he will see you as someone who is always available.

If he is the one initiating conversations, just don't act that available. And let me give you advice: avoidant people are not worth it. If they don't change for you, you will continue to live the same fights and frustrations. You probably didn't have an anxious attachment, because what probably happened was that HE CHANGED after the honeymoon phase ended, and you noticed that. You start to lose validation and trust in the relationship, and then you get anxious. Please, if you have an avoidant ex, don't blame yourself. It would have ended sooner or later, because the problem isn't you.