Gender differences are crucial to understanding Trifles. Mrs. Hale killed her husband because he had cut her off from her community and trapped her in a domestic servant role as his wife.
In investigating the homicide, the men (sheriff, the local prosecutor, and a neighboring farmer) are condescending, linear-thinking, and only see the world through male eyes: they take the feminine domestic role entirely for granted.
Meanwhile, the women in the kitchen piece together the motive from the subtle clues left behind by Mrs. Hale in her kitchen. Whereas the males are report-talkers (focus on facts, information that establish status), the women are rapport-talkers (focus on intimate details that build relationships).
So says Enotes:
In simple terms, Trifles suggests that men tend to be aggressive, brash, rough, analytical and selfcentered; in contrast, women are more circumspect, deliberative, intuitive, and sensitive to the needs of others. It is these differences that allows Mrs. Peters and Mrs. Hale to find the clues needed to solve the crime, while their husbands miss the same clues.
Meanwhile the women, perhaps sensing the gloom and terror in the house, enter timidly and stand close to each other just inside the door. They are partly identified by the roles their husbands play. An important detail is they are always referred to by their married names only, and no first names are used.