I believe that the need/desire to be prescriptive about language comes mainly from a wish to standardize language, that is, to create a framework that everyone can follow (i.e. grammer) and through which everyone can communicate more seamlessly and without issues of misunderstanding or lack of understanding. This would naturally make communication with others much easier. This is what I imagine would be the motivation for someone like a schoolteacher teaching English.
I could also imagine though a desire to be prescriptive about language could be less abstract. For example, a want to be prescriptive about language could come from the desire to perhaps emulate the accent/dialect/general speaking and writing conventions of the upper class, so that someone appears more “elite”, or another example could be based more in politics, with the government passing laws about how to say certain things in order to create certain impressions within the population. (i.e. retaining power through manipulation of official language, banning certain words, changing certain syntax to sound more like a different language, etc.)