For the law to hold perfectly and describe prices, everyone in the market (both buyers and sellers) must be a "price taker". That is, the amount anyone supplies(sells)/demands(buys) is entirely a function of the going market price of whats being traded, and no one believes they will influence prices. (If anyone isn't a "price taker", then supply/demand of the good being traded are no longer the only variables in the function of price). So, typically under competitive market conditions (that is there are many buyers/sellers), as prices rise demand from buyers will drop and selling increases from sellers, whereas the opposite happens when prices fall.

However, in captive markets such as one consisting of a monopoly seller, the seller can test demand to find the most profitable price for them specifically. At which point the seller is no longer operating as a "price taker", as they will reduce selling as prices rise to find that optimal price point for themselves (as they have input costs which have their own price curves that buyers don't know or care about). Remember, a "price taker" cannot influence the price, but must take or leave it depending on price. Thus price is no longer determined purely by the market supply/demand of the good, but also profit margin of the monopolist.

> Huh? Supply is characterized by being "for sale".

It often is, and there is nothing wrong with it being defined that way. But the idea which is being expressed here is what is important. For hyperbole, if I hoarded all of the worlds water, but only listed 2 liters of it for sale (much less than the population needs), would that indicate the world has a water shortage? One would argue yes, if you defined supply as "for sale", but no if differentiated in the way I did.