The three conditions
In every case described above only two forces were applied to the body. And in every one of them the two forces satisfied the same three things.
1. Magnitude
The two forces must be equal in magnitude.
2. Direction
The two forces must act in opposite directions.
3. Line of action
The two forces must act along the same line.
Where the third condition gets forgotten
The first two are easy to remember. But what happens without the third? Two forces that are equal and opposite but act along two different lines leave the body going nowhere — and turning.
This is already familiar
That is the couple of chapter 11 — two forces equal, opposite and parallel but not collinear. Such a pair turns the body without taking it anywhere. So it is not equilibrium.
Equilibrium under two forces
For a body to stay in equilibrium under two forces they must be equal in magnitude, act in opposite directions, and act along the same line. Drop any one of the three and it is not equilibrium.