*Shudder*
Until recently, I spent a good deal of my working life as a butcher. This is the first time that blood has made me squirm. So, congratulations.
Furthermore, this was an interesting take, intentional or not, on the homuncular myth, which I studied recently in a Uni Seminar. Essentially, the homuncular myth began as the idea that there is a perfect man inside every male seed, and that the only thing preventing the creation of a perfect man is the negative influence of the female womb, which turns it into a woman or an imperfect male.
A lot of homuncular stories revolved around removing women from the equation, in creating artificial wombs, using bits of animal tissue, or various other incubatory devices. (I don't know if you can find it, but "The Man-plant: Or, Scheme for Increasing and Improving the British Breed" By Vincent Miller, is a pretty good benchmark, and involves as creepy an individual as the barber who is endeavoring to to create a British Ubermensch, part of which required setting up his young housemaid to get pregnant with a virile specimen from town. Of course, he made sure to observe act in secret because...er... SCIENCE!!) . Some of these stories would claim that this was for the benefit of women, since these stories and interests were of an age when childbirth was arguably a death sentence, but it's impossible to separate it from sexist, patriarchal roots.
Thing in the Bucket was interesting in that the story was actually trying to refine perfection, which the barber ultimately saw as inherently female. Instead, it's the bestial traits that he seeks to weed out.
As well, considering the origin of homuncular myth, I can't help but wonder if there is more to the barber's relationship with his blood bucket than the author describes, especially since it becomes a vision of himself.....