The question here is adding a blemish to an already blemished - by being sick - animal. There are two similar situations where everyone agrees that it is forbidden. If one bakes a leavened flour offering, he is adding to leavening, and is thus liable. If one further castrates a male animal, adding to an existing castration, he is liable. In the case of a firstborn, the strict rulings are based on the Torah verse "there shall be no blemish," and the lenient ones - on "it shall be unblemished to find favor," meaning that if it is already blemished - then it does not find favor.
Art: Winslow Homer The Sick Chicken
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