My ex boyfriend tells me he still cares about me..

We just broke up about 3 weeks ago. It was a relationship over a year. He told me that he still cares about me and still likes me, but we both agreed that we just needed time apart. Well ever since we've been broken up, we've still hung out a lot. Kissed, cuddled, etc. Acted the same for the most part. Friday night I asked him if he thought we would go back out, he said yes. We didn't talk at all Saturday. Sunday night i texted him and we were just talking, joking around i said "So did you miss me yesterday?" And he replied, "yes." Long story short.. We got into a stupid fight. And I told him last night that if i should move on, then tell me because I don't wanna be wasting my time. He told me that he wanted me to find other guys. I said "If you seen me with another guy, you know it would break your heart" And he said "Yeah, it would" So I asked him why he wanted me to find other guys.. And he never replied. And we haven't talked since then. Should I just give him his space to make him realize that he will miss me? Or what should I do?