How are portrayals important to history writing?

Portrayals is has a wide meaning in the context you have given here. I am going to go with the view that maybe you mean 'Why does who wrote about the history we learn about today in school matter?' (If I am wrong do get in touch). In this context, my answer would be that, certainly pre 1950s history, the majority of history and documentation of said history was written by a certain demographic, for example, middle-class, educated men. As a result, their portrayal of certain events and figures within history is important, as not only does it offer a perspective (any perspective is important in history), but it tells us about society at the time. If you would like more help regarding this, please do not fail to contact me.

A perception fraught with supplications of control and portrayals affecting the attitude of any history writers