The Professor wrote:
a failed engine a/c which has a sink rate higher than its climb rate with the engine working would never be in a position to turn back
...and he clearly hasn't considered runway length, wind speed and direction, or the possible desireability of getting back to the airfield over, say a landing on water. It is climb angle, descent angle (both taking into account wind speed and direction and pilot actions), and airfield environment, that count.