Bunnyhugs has an entertaining history of the Daiquiri …
When squeezing the limes extract only the juice and nothing else. You do not want oils from the skin to get into the drink. This is where the Daiquiri differs from the Caipirinha. In a sense the Daiquiri is a purer drink, free of bitter citrus oils, while the Caipirinha is its rustic cousin in which everything is simply muddled together. Ernest Hemingway was the ultimate Daiquiri drinker, and his Daiquiris were free of citrus oil, so keep the oil out! Hemingway’s regular Daiquiri haunt was the El Floridita bar in Havana, where great pains were taken to keep the drinks free of citrus oil. Constante Ribalaigua Vert (known as Big Constante), who ran the El Floridita when Hemingway was a regular customer, was described by the contemporary cocktail writer David Embury as follows: “His limes were gently squeezed with his fingers lest even a drop of the bitter oil from the peel get into the drink; the drinks were mixed (but not overmixed). . . The stinging cold drink was strained through a fine sieve into the glass so that not one tiny piece of ice remained in it. No smallest detail was overlooked in achieving the flawless perfection of the drink”. If Big Constante took such pains to keep lime oil out of the Daiquiris he served Hemingway, I know how I want my Daiquiris made.