Should I be friends with my "ex"?

Background: I was his rebound and didn't find out until it was already too late. He had just gotten out of a long relationship before he met me and was using me as a temporary replacement, I guess. He lovebombed me for about a month or two and took huge steps (multiple dates, meeting my parents/family, came over for Thanksgiving, convinced me to go to Spring Break where he was going, told me I could call him my boyfriend), but then around winter break, he lost interest because he started questioning things and used the excuse that he was busy taking the MCATs. He said he still wanted to get to know me, but I denied that request and he was adamant that we remain friends, even though I told him that's not what I normally do. I was reluctant, but I gave in.

When spring semester started, he was texting me constantly, almost everyday. I still hadn't adjusted yet, so I told him I need to text him about something, but he had to have a phone conversation. I told him I'm still sensitive about the situation and I need time to heal, but he decides to tell me that he wants me to move on and he's texting me because he knows I need support since I lost him (whatever that means). Also, he added that this girl I don't like bought him a drink, his high school crush and another girl paid him attention at the bar, which excited him, and he's hanging out with a lot of people and teaching them a drinking game I taught him. He texted me again the next day and I told him I still need the break.

So should I be friends with him? He definitely came off as extremely insensitive, but I don't know if he was doing it on purpose. I know his relationships with all of his female friends are like this. They discuss who their dating and stuff, but I don't know if it is realistic for us considering we weren't even friends before we started dating. Should I give it a try or just tell him that I can't be his friend?

Side note: I'm also most likely going to see him on spring break.
Should I be friends with my "ex"?
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