A parental cost benefit analysis probably came into it; paying for private school comes with many more benefits than paying for transport to take your child to a state school for many, particularly when the latter can be funded.
Additionally, we have no idea if this child has a bursary, or scholarship or if the dad's company helped with school fees (which many security companies who deploy ex-army professionals abroad do).
The parents would have had to cover the annual school increase, the newly added VAT, and to have done this for three children. Perhaps they thought that keeping their young children in private school whilst moving their eldest to a state school would have meant a more level playing field between siblings (something that mums net are so pro).
Why should a woman have to give up her job so her children can attend state education? That is so detrimental to the entire family, particularly when you think of sex equality and health equality.
We have no idea if there was additional change in family finance, ill health, caring responsibilities, mortgage increases that prompted this to be a quick decision the family had to make.
There are too many unknowns to judge, but a woman should not be told by society to give up work to ferry their child to school - women are already in a very unpredictable and often vulnerable position in society, earning an income is one of the best things they can do for themselves.