The parent is assuming that you can always sell your option to someone else for its fair value. If that's the case, there would never be a time where it's optimal to exercise a call option, because the optionality will always make the option value higher that the value of owning the stock.

This is shown in the article: the curved lines representing the option value are always above the straight lines of the final option payoff (the value if exercised).

This is not necessarily true for put options or for call options if the stock pays dividends. In those cases the option value can be below the payoff line and early exercise would be better than selling the option.