Craig on an infinite old universe

I listened to some of the podcast of the Craig-Law debate.  Craig's argument is in stages.  (1) An argument that the world had a beginning in time. (2) That the world therefore had a creator (3) that this creator is good (4) that this good creator is the very being whose son is the Jesus who was resurrected.

Taking the first, I was surprised by his arguments about an infinitely old universe.  He seemed to be arguing that there are parodoxes associated with a denumerable infinity. For example, if you take away all the odd numbers, you are left with infinitely many even numbers, so an infinity subtracted from an infinity still equals infinity.  Is this a paradox, or just a feature of infinite domains?  He seems to acknowledge this, but then says that this means that infinity is simply a mental construct, and nothing real.  Therefore an infinitely old universe, which would have to be real, cannot exist.  That is also odd.  Most mathematicians, who are Platonists to the core, would hold that the natural numbers are real, but have no difficulty with the 'features' associated with a denumerable infinity. 

Did anyone else find this odd?