That is correct as far as it goes. But CFC molecules are very long-lived and are not washed out of the atmosphere. In time they spread evenly. It takes anywhere from 1 to 6 years for a CFC molecule to make it into the stratosphere, plenty of time for even distribution.
Since almost all the CFC's come from the northern hemisphere, there would have to be a whopper of a mechanism to preserve CFC's all the way to the south pole when almost none get to north pole.
First of all, there is a 'whopper of a mechanism.' CFCs are virtually inert in the lower atmosphere. They are not destroyed or washed out.
Second, I misspoke if I implied that there is a greater concentration of CFC at the north pole than the south. I was just trying to make a point about possible mechanisms. In fact, CFCs are fairly comparably distributed across the latitudes. It is the different meteorological conditions at the poles which lead to difference in ozone thinning. Here is a FAQ that specifically deals with the issue:
Ozone Depletion FAQ Part III: The Antarctic Ozone Hole