Pain, in an of itself, is not a good thing. The actions taken as a result of pain can be good: motivation to fight off an attacker, bringing the family together after a tragedy, etc.

The linked story? Euthenizing the cat was the most humane thing: the ending of life before the good was outweighed by the suffering. That's more of a right-to-die than a pro-life/pro-choice, in my opinion. Is it the most moral choice? The most ethical? Depending on your beliefs, yes.

I agree with your statement that the short painful life of the child is not a wonderful thing. (Though, if you want to argue, I can say it's a good thing.)