Glaspell's decision to begin her story with John Wright's murder and Minnie Wright's subsequent imprisonment rather than with the murder itself enables her to stress more effectively the tension and fundamental differences between men and women.
When the men (district attorney, sheriff, and witness) discuss the crime scene, they do so in a very detached manner, disregarding small details that might hint at a motive (what they so badly need to prove Minnie's guilt). In contrast, the women are viewed as harmless annoyances by the men and left to their own devices in "a woman's world"--the kitchen. This opening allows Glaspell to establish early on how differently the men and women view the murder and the importance of various items.
Likewise, Glaspell includes the conversation between Mrs. Hale and Mrs. Peters about young Minnie v. married, isolated Minnie right before they find the motive evidence (the dead bird) so that readers and the female characters will uncover Minnie's motive before the men reenter the story.
Overall, Glaspell's structure lends itself to one of the story's themes--gender roles.