You are a master of obfuscation.Honestly, you guys should talk more. You can't both be right, right?
The State funds a higher pupil teacher ratio in private schools than it does in public schools.
In order to bring that level down to the same as it is in public schools those private schools fund the cost of those extra teachers from the fees they receive.
If the State was running those schools they would have to fund those extra teachers from general taxation.
The state would also have to fund the upkeep of the schools and all other costs relating to the running of the schools which are now funded by the State.
Remember that our education system is a voluntary opt-in system for schools so every private school can choose to stop being private and hand over the running, and funding, of the school to the State.
Most schools which are private remained out of the system so that they could maintain an individual ethos. That's why they are usually run by a religious order or are a non-Catholic denomination.
Personally I'm not a big fan of them but as long as the Catholic Church, and by extension the head of State of a foreign country, has the ultimate say in so many aspects of how our schools are run I'm glad parents have the choice.