According to Guns, Germs, and Steel, how does Pizarro's capture of Atahualpa explain why Europeans colonized the New World instead of Native Americans colonizing Europe?
To answer this, look in Chapter 3 of Guns, Germs, and Steel. Specifically, look at p. 74 in the paperback edition of the book. There, you can see a heading in italics that reads “Why did Pizarro capture Atahuallpa?” In the next two pages or so, you can see the answer to this question. Diamond makes two main points in these pages.
First, he says that guns and steel weapons (and armor) gave the Spanish a huge advantage over the Incas. He says that guns weren’t that important in this particular case but that steel weapons were. He says that they “slaughtered thinly armored Indians.” He then goes on to say
In contrast, Indian blunt clubs, while capable of battering and wounding Spaniards and their horses, rarely succeeded in killing them.
In short, the Spanish had weapons that could cut through the Indians’ armor and armor that could withstand blows from the Indians’ weapons.
Second, Diamond says that horses made a huge difference. He says that foot soldiers were never able to “defeat cavalry in the open.” Horses simply made the Spanish too maneuverable and too able to run down individual Indians and kill them.
Thus, Diamond says that Atahuallpa’s capture showed the importance of steel weapons and armor as well as the importance of horses. The fact that the Spanish had these and the Indians didn’t was one reason why the Europeans conquered the New World and not the other way around.