IF the gate was unreasonably dangerous or unsafe in some way--such, as for example, it was damaged so that sharp edges stuck out, or so that you had to apply an unreasonable amount of force to open it--then you might have a legal claim against the school. But if there was nothing intrinsically dangerous about the gate and this was simply an accident, as happens, you would not have a claim; liability, or the obligation to pay for another's injury, depends on fault, and if there is no fault on the part of the school (such as from negligently, or carelessly, failing to repair obvious and dangerous damage), there is no liability.