You are wrong and the teacher is right.
If this experiment were in a vacuum, the water would fall while simultaneously evaporating. Surface tension is a fairly weak force and can't make objects magically float.
The surface tension of water is only 72 dynes/cm, but air pressure is 1,013,250 dyne/cm2. Although the units aren't equivalent because surface tension is only measured over one axis, you can see the extreme disparity in the amount of force. If we want a rough guess of the force of air pressure over a single length we can do sqrt(1013250) = 1006.6, which is more than enough force to break surface tension. But the thing is air pressure is usually a compressive force rather than a tensile one, so it usually works in concert with surface tension rather than against it.
The "negative pressure" in the jar is only a negative pressure relative to normal air pressure being considered 0. That vacuum has an absolute positive pressure, pressing down on the liquid. It's just not much compared to ambient air pressure.
The biggest reason why the water falls out when the jar is tilted is due to the force vector of air pressure no longer being completely opposite to gravity.