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It's also often only an aversion to new risks so with travel to/from school the risks created with car use often are maintained while risks associated with the prospect of students cycling are challenged with much greater scrutiny.
I know a school that during the 00s built a flight of steps in an entrance redesign to make it more difficult for a parent cycling a child in with her recumbent and a child seat. After seeing that I kinda accepted that some schools will do anything to discourage cycling.
The biggest harm of this is not so much the day in and day out cyclists but fair weather cyclists and kids+parents who for a few days over the summer might cycle but won't as it's too much faff dealing with the school for just the odd ride. It can be very damaging as those odd rides are what can turn into habits after they experience how short/easy the cycle can be.
There is a lot of misunderstanding about cycling, often by people who who have an elaborate view of education. The misguided risk aversion (as opposed to positivist risk taking) is rife in education (remember the conkers thing) and the Health Services (which focuses on what people can't do rather than finding out what they can do).
Also many schools and Local Authorities will also not allow pupils to ride unless they are wearing a helmet...