Recently the European Judo Union posted the video below on their youtube channel:
This video is a terrific animation of the idea that by enrolling your child in Judo, you are teaching them an important life skill. Judo can be thought of in the same way as swimming lessons.
You teach your child to swim so they can be safe in the water, you teach your child Judo so they can fall safely.
Most experienced Judo participants and coaches will have anecdotes about falling and not getting hurt. In Judo we learn how to fall forwards and backwards and not get hurt. That might be tripping over a tree root in the woods (this happened to me last year) or falling of your bicycle Judo will teach the skills that can save you from minor and major injury.
You may want to consider a adult beginners course to learn breakfalls (Ukemi in Judo terminology), which might be a good way for you and your child to enjoy Judo together too.