Second (and I realize these are flipped), not all people do lose rational thinking ability during stressful situations, but the average person does, and that is where we base most of our legal standing from, what a reasonable, rational person would see as the right thing to do in the situation if they were actually thinking about it without the emotional burden of having their loved one in that situation. Would you go in for a complete stranger in the same situation? Probably not. But if you were trained as a firefighter is would you? Hopefully, and that is the point.
Third, soldiers are trained to do those things and they don't have someone else on scene who is better trained. It is why we, as sailors have basic firefighting training and then do many shipboard drills on fires, because there is no one else to fight those fires, just us. We are trained to save people, to put out the fires. Watchstanders in my own job had the initial responsibility to know how to fight the fires (including what kind of fire we had).
The rescue workers didn't give up. I proved in another post to another person that they in fact brought the boy out of the house still breathing (according to the father). So they simply had to wait til they could safely make it in. Waiting for a safer time is not "giving up", but rather not doing something that will hamper actual legitimate efforts to rescue someone during a fire.
I wasn't talking about this guy. You act as if the police or firefighters knew the outcome we now have from the getgo. They don't. They know only what is going on in those moments. Since it isn't likely that anyone in their pajamas can provide proper identification (although this is a good indicator that the guy likely is who he says he is), it also is possible that he might not be an actual member of the household. Why let him go inside? Because he is emotionally distraught and is probably telling the truth? Because he wants to go in? What if he were a firebug trying to make the situation worse? My point is that at a given scene, the emergency responders do not have the same info that we, as the public, get a day, two, seven, later. They have to ensure that things are not made worse to the best of their ability.