The other argument is that it inflames and encourages desire to assault children in a significant subset (in the sense of risk; i.e. the population doesn't have

The other argument is that it inflames and encourages desire to assault children in a significant subset (in the sense of risk; i.e. the population doesn't have to be large, only the risk) of those who consume it, and that it does so in a unique way, compared to other forms of media. The other argument is that it's a particularly grave violation of the child's privacy, one they cannot consent to. Alternatively, we could just bite the bullet and conclude (perhaps rightly) that maybe porn in general has the same negative effects we allege CP to have. I'm not sure if that's true, but if it is, then I think it would make a good case for banning it.