One difference is that a bicycle accident is an accident, whereas contact sports it is part of the game to hit each other. So it's less a question of whether a rare event might happen to you, and more a question of what is this common event doing to me?
The difference here being the cyclists are not purposely driving their bikes into cars/objects vs being rugby being an actual 'contact sport'
The parent is being downvoted for a "what about X?" response but I think it is actually a legitimate question to ask. Almost every elite sport carries with it serious health and safety risks.
But to counter their concern I would argue that elite sports almost always carry health risks, may amateur sports do not and are broadly beneficial. Contact sports such as American Football, Rugby, etc however are in a different class where the amateur athletes are also putting themselves at significant risk.