What does it mean to "commit paedophilia"?

You commit a crime. Pedophilia is an attraction to people below puberty. It is not actions. Molestation is a crime, possession of CP is a crime, many things are crimes. Pedophilia is how you think, if that was a crime it would be a thought-crime.

I don't even understand your analogy about shooting up a mall, I don't get the connection.