I am telling you why the need of the person to be saved outweighs the need of the dog.
In which case I disagree.
Supposing in your scenario there is no person around to save either human or dog. The people left behind will grieve, they will face trauma, but they do not rely on the lost person for their survival - even children will have someone else step in. They do not
need that other person - humans can survive horrendous loss.
The reason why saving the human is the right thing to do is because of our complex emotions and social structures; there is more devastation to others caused by the death of a person than the death of a dog. In choosing to save the dog first I would be inflicting harm on others, and that is why it is wrong.