Also, the definition of torque is "a measure of the effectiveness of such a force that consists of the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation", so your teacher obviously doesn't know the definition of what torque is.
The formula that your teacher is referring to, T=nBIAcosθ is the AREA of the coil, hence the 'A', not the coil itself. There is a different between the AREA of a coil and the coil itself! When the AREA of the coil is parallel to the magnetic field then its Torque is a max, ie, when the coil is perpendicular to the magnetic field, the torque is a maximum.
So if the coil is perpendicular to the magnetic field, then the torque is always a maximum! As per the definition of Torque
To explain this better, recall T=Fd... Force is maximum when coil is perpendicular to the magnetic field, and distance is pretty much the same, so Torque is maximum when force is maximum which is when the the component perpendicular to the magnetic field is a maximum.
Is there more than 1 Physics teacher at your school? I'd definitely take this further.
