Where did you get that idea from?
One of the aims of Díaz's account is to correct and criticize other accounts of the conquest, especially those of Cortés's ally, Francisco López de Gómara. Time and again Díaz singles out Gómara for criticism. "But above all, he is angered by the heroic halo with which the account surrounds Cortés, in detriment to his soldiers [...] Gómara is his obsession. Unfair to the soldiers, only thinking of Cortés" (Manuel Alvar, 128; translation mine).
Why would Cortés write a book criticizing Gómara's glorifying account of the conquest? Cortés was well aware of the glory he received for being the conqueror of Mexico. He wrote letters to emperors and kings, which used few Americanisms and often avoided giving things specific names. Not so with Díaz, whose work is full of Mexican words and who presents a story not fit for kings, but for the common man, like those who participated as soldiers in the conquest. In this sense, Manuel Alvar can say that Díaz gave life to the modern autobiography.
Alvar, Manuel. In Historia de la literatura hispanoamericana. Vol. 1.