Anthropological Explanation
The Headless Chelsea or mule may be a personification of the latent paganism of some popular practices echoing in the collective conscience of a people massively indoctrinated with a simplistic view of Catholicism. It showcases the wild instincts and repressed behaviours that are unacceptable in a Judeo-Christian society. There may be some connection between the Brazilian Headless Mules and the witches which the Church burnt wholesale in Western Europe.
Being personified as an animal implies a negative view of the character, which embodies the deepest forces that are part of the human consciousness, namely the libido, whose sexual aspect is traditionally associated with the horse, a symbol of sexual potency and brutal feats.
The absence of a head may be a metaphor for the lack of reason, or evidence that the curse involved the perdition of the soul. In either case, without the head to give direction, the body is left under the power of violent passions, immediate impulses and selfish desires.
The most frequent cause for the curse is a woman's unchristian love for a priest, a vicar of Christ on Earth. This association shows the lengths the Church went to indoctrinate people (both priests and women) about the importance of celibacy.
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