Why do villagers think my healing spell is a fire spell?
As pointed out by @Paul and @Armadillo, this was due to me dual wielding an Orcish Sword of Scorching in my right hand while casting a healing spell in my left. It wasn't the healing spell that triggered this response, rather, it was the sword (even though it ran out of the enchantment, it still triggers this same sort of response). See here for more information.