Unfortunately, the male/female relations in "A Jury of our Peers" were typical of that time. How women were able to be treated is best seen through the evidence, the "trifles," which are discovered by Mrs. Hale and Mrs. Peters and dismissed by the men.
Women were not to be persons in their own rights Obviously Mr. Wright was furious at the singing of a bird, at the idea that his wife might interact with the outside world, at the idea that his wife coulod have a life and friends aside from him. He wielded the power and she was to be a silent, submissive woman.
Men were always right and superior. Obviously the clues to this murder are all over the house and in plain sight; the men, however, think they know best what kinds of things are clues/evidence and in what kinds of places those clues would be found. They laugh at the women and dismiss them at every turn.
Because of these two things, Mrs. Hale and Mrs. Peters conduct their own infomal trial and act as Minnie's jury--and they obviously find her not guilty.
The men in this story are condescending towards the women. They think that they, as men, will find the answers they are looking for and the women are there simply to collect Mrs. Wrights belongings. They think anything the women discuss or might find will be trivial or insignificant. They make fun of the women talking about things women are interested in, like quilting and making preserves. The men feel that women are simply an extension of them, with no rights or opinions of their own. That the women could not possibly even know what a clue was if they were to stumble upon one. The men don't think to look for clues in the kitchen, because that is a "womans domain" and couldn't possibly have any significance to the case. The women on the other hand, know that a womans kitchen was the most important room in the house to her and are able to come upon "trifle" clues that let them know what was really going on in the Wright home.