Which term describes the painless killing of a suffering animal due to an incurable condition?

The term that describes the painless killing of a suffering animal due to an incurable condition is euthanasia. This practice is conducted with the intention of relieving the animal from pain and suffering, often when their quality of life has deteriorated significantly due to illness or injury. Euthanasia is typically performed by a veterinarian using approved methods to ensure that the process is as humane and painless as possible.

In contrast, other options do not pertain to this specific context. Extinction generally refers to the end of a species, not individual animals. Termination can be a vague term and is not specific to animals; it might be used in various contexts without indicating the humane aspect of ending suffering. Neutering is a surgical procedure aimed at preventing reproduction and does not relate to euthanasia or the alleviation of suffering. Therefore, euthanasia is the most accurate term in this scenario, as it specifically addresses the compassionate choice to end the life of an animal in a painless manner when facing irreparable suffering.