electromagnetic induction I don't understand?

You are wrong. There is induced emf in both cases, i.e. in a single wire and in a square coil.

Suppose the magnetic field lines are pointing in direction into the paper, the single wire and coil are moving from left to right across the field lines. For the single wire case, emf is induced, with the upper end of the wire be +ve and lower end -ve.

A coil can be considered as two single wires joined together (by another two wires). In this case, the two sides of the coil (i.e. two single wires) that are cut normally across the field lines will have emf induced. Because the two sides of the coil are moving in the same direction across the field lines, you could visualize that the upper end of each wire be induced +ve, and the lower end be -ve, similar to the single wire case above.

As a result, the upper side of the coil is at a higher potential than the lower side. In other words, the upper side is induced +ve and the lower side -ve.

I think what you have confused is why there is no induced current in the square coil. As you can see that both the left and right hand sides of the coil have induced emf of the same polarity (i.e. both have +ve at the upper end and -ve at the lower end), there is no circuit for the charges to flow. This situation is just similar to two cells connected in parallel. The cells are analogous to the left and right hand sides of the coil. Imagine that you use a wire connecting the two +ve poles of the cell (analogous to the upper side of the coil) and another wire connecting the two -ve pole of the cell (analogous to the lower side of the coil). There will not be any current flowing though there is emf on the cells.