On the surface, the woman in "The Snake" wants a male rattlesnake to which rats will be fed and which will be kept boarded at the laboratory on her behalf. She does not want it as a pet at home. It may also be inferred from her repulsive swaying motions (Dr. Phillips thought he might be made ill) that she wants some exotic association with the snake on some undefined but apparent psychological level.
Related to the psychological level, there is no appreciable evidence in the story from which to infer the woman's motives or the psychological impulses that compel her actions and requests. Critics protest that when questioned, Steinbeck insisted that the story existed at the surface level only because it was drawn from a true-life experience witnessed by multiple people that happened to Steinbeck's friend and sometimes collaborator Ed Ricketts.
If a deeper explanation to what the woman wanted and why she wanted it is needed, then the reader must use independent conjecture to analyze the story as a psychosexual story in the vein of Freudianism or as a symbolic allegorical story or as a Jungian primordial universal archetype story. In other words, when all textual evidence as to deeper meaning is lacking, then the reader is free to analyze it according to preferences in literary theory and aesthetics. According to Masterplots II:
John Steinbeck contends that he has told this story exactly as it actually happened in his friend Ed Ricketts's Cannery Row laboratory and denies knowing what—if anything—it means.
However, in an analysis from the point of view of any of the three critical perspectives mentioned above, what the woman wants and why remains elusive. What may be seen less elusively is the dichotomy established by Steinbeck's story between respect for life (Dr. Phillips who condones valid scientific experimentation but not cold-blooded maltreatment of creatures) and callous disregard for life (the woman). But even this doesn't illuminate what she wants and why she wants it, except to say that she wants the experience with the snake to satiate some wanton inner appetite. [Any of Random House Dictionary's first four definitions of wanton might apply: 1. malicious, unjustifiable. 2. without motive or provocation. 3. careless; reckless; without regard for what is right or humane. 4. morally lawless and unrestrained.]