Thanks for all the responses guys!
Some things are relevant to this discussion which has not been mentioned by any of you so far.
Normally, depending on atmospheric conditions, the safe altitude in a C-172 is around 500-600 feet. At 500-600 feet I am able to turn the airplane around and land on the opposite runway after a simulated engine failure.
As I already explained earlier, if I fly out at Vy, I will get to this altitude quicker, and therefore I will be "unsafe" a shorter period of time. If my engine fails exactly at safe altitude while climbing at Vy, a climb at Vx would not allow me to safely turn back to the runway. Therefore I would be forced to land straight ahead whereas I would be able to turn back if I would have climbed at Vy.
Some arguments my fellow instructors use to explain how Vx is better is to say that once you get to safe altitude Vx will make you closer to the runway. This is true, but the way I see it having an engine failure is not a function of altitude, but rather a function of time. Either way, unless you take off from a really short runway and with a tailwind, I am fairly certain that safe altitude at Vy will allow you to reach the runway after the turn back (assuming a C-172 or any other light single engine airplane).
Either way what I just wrote and all the other arguments for using Vy rather than Vx obviously makes Vy seem like the best choice.
Any further thoughts or comments to what I just explained, or would you mostly agree?