Why there is no supply on monopoly markets? We learned in the class that monopoly markets do not have supply curve. Our textbook (Microeconomics and Behavior, page 388 from, R. Frank) says:

A monopolist has no supply curve

and it explains it by saying:

The reason is that the monopolist is not a price taker, which means there is no unique correspondence between price and marginal revenue when the market demand curve shifts. Thus, a given marginal revenue value for one demand curve can correspond to one price, while the same value of marginal revenue for second demand curve corresponds to a different price. As a result, it is possible to observe the monopolist producing $Q_1^*$ and selling at $P^*$ in one period, and then selling $Q_2^*$ at $P^*$ in another period.

I don't get this. We learned that in competitive markets demand can change from period to period even if the price stays the same (like when supply is just horizontal line). Also, why can't we just pick one point in time look at possible combinations between P and Q on monopoly market, and call those combinations supply? The book has some examples but they don't explain this clearly.
The argument is that the monopolist's decision is based on the demand curve (in effect matching marginal total revenue to marginal cost) so is not independent of the demand curve, and in that sense there is not a corresponding supply curve with price and quantity in equilibrium where the two curves cross; the monopolist equilibrium point is likely to be at a lower quantity and higher price.
The conventional demand curve illustrates the price against quantity.  If instead the demand curve illustrated marginal total spending against quantity, then where it crossed the supplier's marginal cost curve would give the monopolist equilibrium quantity (though not the equilibrium price), and in that sense the monopolist's marginal cost curve could the be seen as the supply curve.