The problem with private schools in Geneva is that there is no collective agreement which would clarify the application of Swiss labour law to the specific employment circumstances and additionally protect the employees.
Such an agreement exists, for example, to protect the employees of creches and other daycare institutions in Geneva and it specifies that teachers have the right to fully paid 7 weeks of holidays per year. One full year of service is counted if the employee started to work at the latest on 1 July of the year.
Even in the absense of such an agreement, general provisions of Swiss labour law apply, which means that, unless hired temporarily, you definitely have the right to 4 weeks of fully paid holidays during the year in addition to official holidays (up to a maximum of 9 days per year).
You can do several things: ask the school administration to show you the exact provisions of the law that justify their action; if you feel comfortable, ask some of your colleagues whether they have the same terms of contract; go to permanence juridique (
http://permanence-juridique-geneve.ch/) with whatever information you find and your contract, and get legal advice or talk to a trade union, for example
http://www.unia.ch/Home.1.0.html?&L=1 or
http://www.sit-syndicat.ch/Sit-présente.htm).
General advice -- try to learn as much as possible about your rights -- although you may think that you will never get into contract-related disputes with your employer, it is better to be prepared. Remember that employees in Switzerland are generally well-protected.