Why did the writer start the story with Miss Emily's funeral?
Part of what Faulkner want to accomplish in his story is break down memory as logical and linear. You'll notice the narrator skips around thoughout the story so that we as readers are often confused concerning the chronology of events. Beginning with end is part of this process. After all, when we remember something, we seldom recall where the event began but rather where it ended--its result--or perhaps with that aspect of the event that had the most effect on us. When people arrive at Emily's funeral they talk of her "as if she had been a contemporary of theirs, ...confusing time with its mathematical progression, as the old do, to whom all the past is not a diminishing road but, instead, a huge meadow which no winter ever quite touches...." In this passage the narrator throws light on why he confuses the chronology of time in telling the story.
In addition to this, it's part of the "hook". Whenever you write a memoir or personal piece of writing, you must make the reader care about it. By beginning in the middle of the action and using a flashback to fill in the necessary background details, you grab the reader's attention right off the bat. Faulkner has done an amazing job of that as we want to know more about who died and why the whole town is so involved in it.