I instructed Bikeability for a couple of years and encountered many versions of the attitude in question. Reasons are usually that the school are (probably unneccesarily) worried about being sued in case of an accident, don't want the worry of kids on bikes mixing with the 4x4 chaos outside the school gates ( ironic huh ? ), have limited space for bike storage so limit cycling to year 6's or want the kids to have Bikeability training before they cycle unaccompanied.
As you are cycling with your daughter then the school should have little argument especially if you are locking the bike up and taking the key away.
If they are still resisting then ask to see the RA or insurance policy that prohibits cycling. I vary much doubt that they'll be able to produce one.
