Simia Saturnalia said:

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So, given that guns aren't armor-piercing, please explain why the gun lead to the phasing out of plate armor.
Because it didn't. Plate armor and guns existed side by side from the 14th century through the 17th century, a period of three hundred years. Gunpowder existed in Europe
before the Battle of Agincourt, the classic battle of French knights and English archers. Plate armor lasted through Cortez's conquest of the Aztecs. Famous forms of armor, such as Maximillian-style plate armor, were not developed until the 16th century, well after the introduction of guns.
In places other than Europe, it is even more interesting. Gunpowder and gunpowder weapons existed as early as the 11th century in China. In Japan, the mass use of firearms in battle predates Bushido and the modern idea of the honorable samurai. The Moghul dynasty of India combined horse-mounted archers and cannons in the early 16th century.
Also, the simple truth is that guns were never an armor piercing weapon. Plate armor was made to resist bullets. The term bullet-proofing comes from the practice of shooting a gun at a breastplate to show that it could resist a bullet. Meanwhile, the English Longbow was just as good a weapon at fighting a mounted knight as the gun, if not better, and the common warhammer was
designed to peel apart armor. As a whole, even if the supposed ability of guns to pierce armor is true, armor-piercing is certainly not unique to the gun.
Plate armor was phased out only after guns became
much more powerful due to radical increases in technology, and for reasons such as the changing nature of war and the movement towards using quickly trained ordinary people as soldiers, rather than wealthy and highly trained nobles. It took the
Industrial Revolution to kill plate armor, not the gun.