Giving space... a good idea?

Me and my ex boyfriend broke up 2 weeks ago. He broke up with me due to various arguments we'd had. (There was only a couple but he is quite sensitive so he took it harder than I did) I basically said if we are going to argue about the same thing over and over what's the point in being together? I told him I loved him, wanted him etc but it needed to be worked on. And he broke up with me. I gave him time to think about it for a week, as he requested. He said he still loves me and wants to be with me he just doesn't want to be hurt by this. After a week, and speaking on and off, he said he was sticking with his decision to break up. After speaking to him, he said he was really clueless what to do now, he was sure before but not anymore.

I told him how much I cared, etc. And he said he appreciated everything I said, but wanted to think again. Is giving him more time to think a good idea? I haven't contacted him since then. It's been 4 days now and he keeps putting lyrics on his facebook to songs that we're "our" songs. I'm really confused.