Simple. When a writer creates something, they no longer truly "own" what they've created, regardless of what copyright lawyers may want you to believe. It takes on a life of it's own, and has the meaning that people tend to assign and read into it... independently of the author. It's likely that even if what the audience senses is correct, it would be on such an unconscious level that the author would be unaware of their own intentions!
What a person is really asking when they say, "analyze the author's intent," is, "if you had written this, and you had lived under similar circumstances as the author, why do you imagine YOU would have written it, and what do you think your motivations would have been?" It's an exercise in empathy, not logic.
I find it particularly interesting, because I've actually spent a lot of time using and examining things like computer programs, art, and writing, trying to get into the heads of the people who created them and understand what kind of people they were. I mostly did this because I was so mistrustful of what people say about themselves directly, that I felt that I needed to look at the things they made as a way of getting access to a level of them behind what they project, that they can't hide or mask quite as easily.
In other words... you can't know an author's motivations, but constantly attempting to guess what they might have been can help you develop better empathy and intuition about what people's motives might be in general. I do know that eventually, the more books, programs, or pieces of art I analyzed, the more "on-target" my analyses tended to become. If it's possible to create something in a specific way, it's also possible to take something apart and figure out how it was constructed, and get a vague clue as to WHY it was constructed.
It's like archeology. We dig up old buildings, but the people who built them are gone... we don't KNOW why they built them, but we develop a sense of human nature that gives us an ability to take an educated guess. The same kind of sense applies to literature, I suppose.
It's about learning how to think in terms of a "good answer" or a "meaningful answer" rather than "right/wrong answer."