In "The Lottery" by Shirley Jackson, why did the lottery officials and people prefer a male from the family to draw?

One of the fascinating aspects of Shirley Jackson's short story, "The Lottery," is the strong adherence to tradition evinced by the actions and words of the townspeople before, during, and after the lottery. Not only are the traditions of the lottery followed uncritically, what conversation that does occur among characters concerning the traditional nature of the lottery is primarily to decry other places that have slipped in following tradition or that have discontinued the lottery entirely. Further, things that disrupt the strict adherence to tradition, such as Tessie Hutchinson's futile protestations over her fate, lead to discomfort and unease among the townsfolk.
One such tradition apparent in the story is that the head of household is responsible for drawing in the first stage of the lottery, the one that determines from which household the sacrifice will be taken. It is also apparent that, traditionally, the head of household duties are performed by the eldest adult male present from the household. This is best shown by the exception that occurs. Mrs. Dunbar has to draw for her husband because he is unable to attend the lottery due to a broken leg and their eldest son is not yet old enough to serve as head of household for the lottery. However, it is clear form the conversation between Mr. Summers and Mrs. Dunbar that it would be preferable for her son to draw instead of her if he were old enough. Further, the "Watson boy" is praised for being old enough to draw for his mother and himself, further showing that, traditionally, the eldest adult male in a family was considered the head of that household, at least for the purposes of the lottery.
Like with the lottery itself, the purpose behind the tradition of a male being the head of household and drawing during the first stage of the lottery is not important. What is important to the townspeople is that the traditions of the lottery be adhered to as closely as possible. Anything else brings to the surface the discomfort and unease that they all seem to feel about the lottery. By following the traditions as closely as possible, including the tradition of the male head of household drawing in the first stage of lottery, the townspeople are able to blindly follow the traditions rather than focus on the horror of the sacrifice.