In addition to other responses, one more approach to the problem is the issue of reciprocity (one of the many consequentialist way to approach the problem).

Simply put, do you want to live In a society where, if it was you versus the dog in the fire, other people would choose to save you over the dog? If you would like to have people save you, you could require or try to force people to do it, but chances are that you won't be very successful because your power, just like every one else's, is limited.

One way you could obtain this behavior from others is by proclaiming it a universal rule ("it is good to choose to save other humans") and show the example by choosing to save people yourself (otherwise, people would judge you hypocritical and wouldn't be motivated to comply).

This goes further than the famous golden rule ("do unto others as you would have them do unto you"), because this behavior would favor most citizens (most citizens happen to be humans, not dogs) and could establish a solid consensus, and we could legitimately make it a rule, a law, to save people and have it enforced by society (police and justice system). Which is precisely what many countries do: in my country choosing the dog could be considered failing to assist an endangered person, and you could go to prison.

So not only is it rational to save the dog, it is rational to make it mandatory by law.

In addition to other responses, one more approach to the problem is the issue of reciprocity (one of the many consequentialist way to approach the problem).

Simply put, do you want to live In a society where, if it was you versus the dog in the fire, other people would choose to save you over the dog? If you would like to have people save you, you could require or try to force people to do it, but chances are that you won't be very successful because your power, just like every one else's, is limited.

One way you could obtain this behavior from others is by proclaiming it a universal rule ("it is good to choose to save other humans") and show the example by choosing to save people yourself (otherwise, people would judge you hypocritical and wouldn't be motivated to comply).

This goes further than the famous golden rule ("do unto others as you would have them do unto you"), because this behavior would favor most citizens (most citizens happen to be humans, not dogs) and could establish a solid consensus, and we could legitimately make it a rule, a law, to save people and have it enforced by society (police and justice system). Which is precisely what many countries do: in my country choosing the dog could be considered failing to assist an endangered person, and you could go to prison.

So not only is it reasonnable to choose to save the human, it is reasonable to make it mandatory by law.