Why does Goemon tell Manjiro that he can
never be a samurai?

Goemon told Manjiro he can never be a samurai for he did not commit harakiri, which is a form of self-mutilation and su icide so as to escape being captured by enemies. Japanese Samurai status is achieved only when a person braves the odds and prefers to die instead of being taken captive or even killed by an enemy.

Explanation:

Heart of a Samurai is a true story based book written by Margi Preus about a young boy named Nakahama Manjiro. The story deals with the life of this young fisherman and his life in the United States, and eventual return to Japan after nearly a decade.

The reason Goemon thinks Manjiro is not a true samurai is because, for him, since Manjiro did not commit sui cide or harakiri (seppuku), he did not deserve to be considered a samurai. He did not like the idea of Manjiro being taken to America, stayed there for almost a decade, and returning back and being honored with the samurai status.