Why does the argument about Jones being mad rely on equivocation?

The argument that "the loss made Jones mad; mad people should be institutionalized; so Jones should be institutionalized" is a classic example of equivocation, a type of verbal fallacy.

This argument relies on equivocation because it uses the word "mad" in two different senses to reach a faulty conclusion. In the first premise, "mad" is used to mean "angry." However, in the second premise, the word is shifted to mean "insane" or "mentally ill." By failing to maintain a consistent definition of the term throughout the logical progression, the argument creates a false connection between being angry and the necessity of being institutionalized. Because the word changes its meaning between the premises and the conclusion, the logical validity of the argument collapses.1