His position, I'm guessing, is that when a good has no natural scarcity (pictures and music in digital form, for example, or compiled code), society should not be creating an artificial scarcity in its stead (ie. compelling others not to reproduce it through force of law). He views the idea of this compelled scarcity to be, basically, rent-seeking behavior codified into law.
I'm not entirely sure, but I suspect the "you can't own" portion of his statement was a point of possession and direct control, not necessarily law.
exratione, please let me know if I'm misrepresenting your position here at all, and I'll correct my post. (I'm intentionally leaving out my opinion, just trying to clarify yours. :))