It seems to me that you are just a little confused about what you want...
Why would you break up with someone and then try to remain friends with the possibility of getting back together?
The first thing that you need to do is figure out what you really want... My guess is that the reason he feels that you're still together is that you're sending him mixed signals - on wonder the poor guy is confused.
I understand that's it hard to break up with someone and to be alone, but that's exactly what you need when you end a relationship - some alone time to allow yourself to heal and to move forward. It seems that you're trying to move forward, backward, and stay in the same place at the same time!
My suggestion is to take a step back and figure out what you want for yourself before you try to establish any type of relationship with your ex. And then be very clear with you intentions whatever they may be (dating, friends, nothing) - no mixed signals. It's not fair to either of you to be in limbo like that...