It’s cruel to exterminate a million humans because they annoy you, yet substitute humans for ants and suddenly it’s not cruel. The subject matters and what is cruel to animals is not necessarily cruel to humans. and vice versa. Put a chain around the neck of your child, drag it to a local field and give it snacks until it learns to roll around on command and the difference should be blatantly obvious.
It could be: cruel to euthanize either
It could be: cruel to let either one suffer an agonizing life
It could be: cruel to euthanize a child, but do whatever you want with the dog
It could be: cruel to let the suffering dog live, but do whatever you want with the child
It could be: do whatever you want with either
It's none of those. Why?
If I can (and must) keep my child alive despite an agonizing and fatal illness, why can't I do the same for a dog? Why do I risk going to prison just for treating a dog like a child? Why am I required to have the dog killed?