Quick question for the English majors: what two components shape an author's reason for writing?

[RobShein]

I'm a freshman considering an English major, and I'm trying to understand some foundational concepts. In my intro to literary studies class, we keep talking about author's purpose, but I'm not clear on what two components shape an author's reason for writing. I've gathered from our readings that it's not just about the author's intention—there's also something about the audience and the context . One of my TAs mentioned that purpose comes from the intersection of the author's goal and the audience's expectations. Is that accurate? And does this apply to all types of writing, from poetry to textbooks? I'm trying to build a solid foundation for my major, so I want to understand this correctly from the start.