It probably doesn't feel great to be outnumbered and fought into a corner. That's probably why American troops tend to avoid those situations.
Or attack in another direction.
You never know what surrender could bring. At best, the unit is just out of the war 'til the end. At worst, the officer in charge might just get everyone killed.
Maybe it's better to risk a fight to the death.
1. "I have not yet begun to fight."
– John Paul Jones, Continental Navy Captain during the Revolutionary War.
While at the Battle of Flamborough Head, John Paul Jones and his combined American and French squadron of ships went head-to-head with large British frigates protecting British shipping.
From the Bonhomme Richard, Jones engaged the frigate HMS Serapis for hours. Each tried to board then subsequently sink their opponent. When the captain of Searapis called for Jones to surrender, he uttered this now-famous reply.
He is the only Continental commander to bring the Revolution to the British, raiding English shipping in the Irish Sea and the English town of Whitehaven.
– The cannon Texian commander William Barret Travis fired at Mexican General Antonio Lopez de Santa Anna at the Alamo.
By now, most Americans know the story of the old Spanish mission in San Antonio. Santa Anna's 1,800-strong Mexican Army laid siege to the Alamo for ten days as an estimated 200 or more defenders held their ground for Texas' independence.
Santa Anna's troops slaughtered the defenders of the Alamo to the last man. He would be captured by the Texian Army days later while hiding amongst his soldiers after losing the Battle on San Jacinto, forcing him to grant Texas its independence.
3. "I beg leave to say that I decline acceding to your request."
– General Zachary Taylor to Mexican General Antonio Lopez de Santa Anna.
President Polk deliberately gave all but 4,650 of Zachary Taylor's troops to General Winfield Scott in an effort to diminish Taylor's growing popularity back home. When Santa Anna learned about this, he sent his army of 15,000 Mexicans to annihilate Taylor.
Instead, Taylor's army routed the Mexicans, despite being outnumbered 3-to-1. Rather than checking Taylor's popularity, the general's military acumen so impressed the Whig Party, they ran him as their candidate for President, despite disagreeing with him on practically every issue.
He was easily elected.
4. "I will do my best to meet you."
– Confederate General James Longstreet's reply to Union General George A. Custer.
Custer threatened to "immediately renew hostilities" just as Lee and Grant were discussing the term of the surrender of all Confederate forces at Appomattox Court House, demanding Longstreet surrender separately.
Longstreet then bluffed that he had many more operational units than he did by ordering imaginary these units forward as he spoke to Custer. Custer balked and withdrew his demand.
– General Anthony McAuliffe, acting commander of the 101st Airborne while surrounded at Bastogne during the Battle of the Bulge in WWII.
Major General Maxwell Taylor was at a staff conference in the United States when strong German armor units surrounded the 101st around the Belgian city of Bastogne. General Heinrich Freiherr von Lüttwitz sent a surrender demand threatening to annihilate the U.S. troops if they didn't capitulate.
McAuliffe's response was interpreted to von Lüttwitz as "go to hell."