You dont disagree with the author. The key phrase is "given the choice" from the consumer perspective. That people who sell will demand the stronger if they have the option isnt surprising.
With a free-floating exchange rate, the buyer wants to use the weaker currency and the seller wants to accept the stronger one. The seller can set prices in each according to his preference, and the buyer can decide which to pay vs. which to save according to hers. The market will discover an exchange rate between the two currencies accordingly, but no economic law dictates that one will drive out the other.
Gresham’s law applies when the seller is bound to a certain rate of exchange between the two currencies. The buyer will therefore pay in the currency she has the least desire to hold for the long term. As a result of everyone doing this, over time all trading will be done in the less-desirable currency.
In practice, you have to settle debts in the government dictated currency. Here Gresham takes hold, the valuable currency will disappear from circulation. Think silver dollars in the US with a higher material value then the nominal value. You still have to accept payment in any dollar so you wont spend silver dollars doing so. As long as you have the choice to sell it for material value. Think copper content in pennies for where this doesnt apply because its illegal to melt down.
Its all just a description of how the market (meaning people ) behaves once the government applies pressure in certain directions.
