My father-in-law painted my bathroom with paint for moist areas, but now a few years later after I tried to take down my shower curtain rod, the drywall and paint peeled off the wall leaving a bad place on the wall. My question is, how do I repair this. It is on both side of the wall where the curtain rod was.

Probably with joint compound, unless the entire thickness of drywall has come off. In that case, I've seen it done where a piece of 1x2 wood bigger than the hole is slipped into the hole, and fastened with drywall screws either above and below the hole, or on either side, and then a new piece of drywall is cut to fit the hole (which you have neatly trimmed to a rectangle shape) and screwed to the wood, and then you apply joint compound.