This week was about countering the opponent. Remember that the main reason to scout (scouting was last week's topic) is to create the chance for you to counter the opponent.
Professor Feng said it's pretty obvious which units counter each other, so there's no need for him to cover all those specifics. There is actually a lot more to say about countering than just listing specific unit counters though. For example, let's say the opponent has 12 dragoons. What would be a good counter? A standard answer is speed upgraded zealots, maybe 14 of them. But then the professor showed us a replay of a match showing this exact situation where the *dragoons* win. In this case, the player controlling dragoons used an extreme amount of micromanagement to dance them around so that even the speed-upgraded zealots had to take lots of damage trying to reach any particular dragoon. After a bit of this, the dragoons get a lead and their superior number spirals to make the fight easier and easier for them.
So even though speed zealots would usually counter, the opponent can use micromanagement to survive the counter. What can yo do against an enemy who does this? The answer is to force him to run out of "attention" resource. Micromanaging the dragoons is kind of hard in itself, but there's no way he can do that while also defending against some other attack (or two!) in other parts of the map.
The next concept is the effects of scale on counters. The two examples were mutalisks versus marines+medics and vultures versus dragoons. Marines+medics are a "counter" to mutalisks, but only when the battle is of a certain scale.