What about the history that says the peasant class has limitations and the proletariat doesn't?

First of all, the peasant class is not the proletariat.

The peasant class in the general sense consists of rich peasants, middle peasants, and poor peasants, and among them the rich peasants and middle peasants are mostly self-employed peasants. These peasants have some means of production (land) and some tools of labor. The proletariat, on the other hand, "has nothing but strength" and is the real proletariat.

Secondly, the reason why it is said that the working class represents the most advanced productive forces is that the working class guides the mode of production of socialized mass production, is the source of all technological progress, and is the driving force in the construction of ****productivism. These words may not be easy to understand, in layman's terms, Marxism believes that the peasant class, because it is not a complete proletarian, it has a way out when the revolution fails, so its revolutionary is not as complete as the proletariat, that is to say, the so-called "barefoot is not afraid of the shoes".