Empirically, I agree with the second ethicist, but from the parent's point of view, it reminds me of the philosophical "trolley car" thought experiment.
The trolley car is a hypothetical in which you witness an out of control trolley car with fifteen passengers that will crash at the bottom of a hill and kill everyone on board. You are in a position to switch the tracks to a track that will slow the car to a stop, but there is a bystander on that track that will die if you switch it. This one is somewhat easy to make since you may be sacrificing one person, though "passively" to save fifteen.
The second variation asks the same question, but this time there is no switch, just a bystander who is large enough to slow the trolley down safely if you were to push him into the car's path. This is morally less acceptable, since you actively kill the bystander to save the fifteen.
From the parent's point of view, they are actively killing one child to save the other. This may not medically be the case depending on the level of parasitism that the weaker twin exerted on the stronger. Empirically, it's easy to agree with the compulsion to perform the procedure, but the parents are also being disenfranchised while acting in good faith to not cause active direct harm to one of their children. This was sure to be significantly emotionally harmful to the parents.