Some cancers are the result of damage. I.e. asbestos in your lungs. Children just haven't punched enough time on the clock to have as many of those experiences. By the time you are old your probability of exposure to at least one of those experiences gets pretty high. That's not aging doing the deed, it's living.

Also, some cancers take time to develop, which would make for fewer diagnoses in childhood.

Well, one of the least ambiguous definitions of aging is "accumulation of damage at the microscopic/cellular level", that includes both accumulation of foreign matter over time (e.g., accumulation of asbestos particles, or cholesterol) and accumulation of damage due to matter or othewise (e.g., damage accumulation due to daily asbestos exposure without asbestos actually accumulating). So you essentially supported my point.

If you have a different meaningful definition of aging I'd like to know.