“People love to say, “Give a man a fish, and he’ll eat for a day. Teach a man to fish, and he’ll eat for a lifetime.” What they don’t say is, “And it would be nice if you gave him a fishing rod.””
The quote "People love to say, “Give a man a fish, and he’ll eat for a day. Teach a man to fish, and…" is famous quote by Trevor Noah (1984), South African comedian.
That’s the part of the analogy that’s missing.
page 190
Born a Crime
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South African comedian 1984Related quotes

This quotation has been misattributed to Laozi; its origin is actually unknown (see "give a man a fish and you feed him for a day; teach a man to fish and you feed him for a lifetime" on Wiktionary). This quotation has also been misattributed to Confucius and Guan Zhong.
Misattributed

“Sell a man a fish and he will eat for a day. Teach a man to fish and he will put you out of a job.”
Ron English's Fauxlosophy (2016)

A parody of the "Give a man a fish..." proverb alluding to the subprime mortgage crisis of the aughts on The Colbert Report (14 May 2008)

Attributed to Marx (possibly in jest) in W. C. Privy's Original Bathroom Companion (2003).
Misattributed

“The cat would eate fish, and would not wet her feete.”
Part I, chapter 11.
Proverbs (1546), Bartlett's Familiar Quotations, 10th ed. (1919)