No, a strong business reason would be that they were unable to find someone to job-share with after reasonable advertising or that they were unable to find solutions to handover (and they would be hard pressed to legally argue that when so many similar schools manage it succesfully).
Employers can reject an application for any of the following reasons:
extra costs that will damage the business (it's often cheaper to employ 2 p/t due to employers NI levels)
the work cannot be reorganised among other staff (it obviously can in the case of a job share)
people cannot be recruited to do the work (they have been in this case and the employer has to at least try)
flexible working will affect quality and performance (it really won't, parental preference will not over-ride the precedent set in many, many other school)
the business will not be able to meet customer demand (not applicable, see above)
there’s a lack of work to do during the proposed working times (would only be applicable of the person requested to work during non core school hours)
the business is planning changes to the workforce (not applicable)