the irony is precisely that no human doctor would ever suggest p

no parents would follow that suggestion. And if they did, they would be seen as monsters by society. But when it comes ot non-human animals, all of a sudden, the life-depriving decision can be made so easily in the name of "poor quality of life." Her question to you doesn't make sense because her analogy is false; she doesn't treat the horse as a human family member.