There appear to be two schools of thought on the topic of riding with children:
Veteran riders, et al: Heck yes! I see no problem what-so-ever with having my kids ride with me when I am out riding for the day. As long as they are wearing protective gear they, too, should get to experience in the joy that is motorcycle riding.
Non-riders: You are out of your mind to even consider placing a child's safety in jeopardy by taking them along on the back of a motorcycle, regardless of the safety gear they will wear. The risk is just too high to justify the "joy of riding" they will get by riding along wtih daddy or mommy.
The arguments, the reasoning, the statistics - all can be skewed in favor of one argument or the other: allow children to ride with you, avoid children from riding with you.
My point of view on the subject is this:
Is the risk greater for your small passenger if you take them on your motorcycle, having equipped them with proper riding gear, taught them the proper passenger techniques of riding, etc, versus taking them horseback riding or rollerblading or bicycle riding? Why do we take them on these greater-risk activities?
The experience, the initial fear and excitement we all feel at the onset and the sense of accomplishment let alone joy of being alive that we derive from these activites is what drives us to pursue these things.
Many will be quick to point out that there is a speed factor involved here that makes the event that much more dangerous.
Remember, a commom factor of an injury related to a motorcycle is the fall to the ground; the vertical travel from the seated height on the bike to the ground, not the horizontal movement (i.e.: moving froward on the road).
Why else is the helmet so important? Why else are accidents so injurious at lower speeds? It wasn't the forward impact in many cases as much as it was the falling from the bike and striking the pavement that had the most severe resulting injuries.
Having said that, with rare exception, there is not a rider that will knowingly ride in a manner that would place a child passenger at risk when riding.
Such riding events tend to be "scenic riding", riding through parks; these slower rides are usually to enhance the enjoyment of being on a motorcycle with mom or dad, sharing in the exhileration of riding on a motorcycle.
The love for riding is to originate somewhere - for us riders, what better time than as a child, with our parents?
And if our children don't like it? If they are scared of riding? Then we simply don't take them on rides - as parents we want to keep our kids happy, right? Until they decide they aren't scared of riding again, maybe a big-wheel will help with the transition.
I entreat you, dear reader, to comment with your opinion for or against children riders.