Should you and your ex know everything going on in each others life if you have a child together?

I think no, only things that regard our daughter. He thinks yes because he “still considers me a best friend”. Given this is the same guy that found out I’m talking to someone, told me to fuck off, then texted me the next day like “you not gonna talk to me?” 🙄🙄🙄 he’s preaching about openness and honesty but I think it’s just a tactic to get to know what’s going on with me because he’s been manipulative and controlling in the past. Am I seeing it wrong?