Why prevent high frequency input into the loud speaker using a low pass filter?
What the professor should have said is: "oscillations may occur, R6 and C3 help prevent this".

If there are oscillations, it's not only because of Q2. I see a feedback (?) line connecting to R5, feedback can cause oscillations if not done properly.

The network of R6 and C3 provide a defined impedance at high frequencies and that helps with the stability of the feedback loop. The loudspeaker might have a high impedance at the frequency where oscillations can occur. This high impedance increases the loopgain of the feedback loop and that helps oscillations. By adding R6 and C3 there is a low(er) impedance at the these frequencies which lowers the loopgain and that prevents oscillations.

So that R6 and C3 are not there to prevent high frequencies from getting to the loudspeaker ! They are there to prevent oscillations and to keep the amplifier well behaved.