It has everything to do both with that example and with the Borders' example. You support cowardice by telling us that real bravery is only justified if it can save or help more people than it might hurt. This is why you support surrendering to Islamists and Nazis as the "logical" thing to do.
No, it doesn't.
The Borders example is a confrontation of two values - what you termed "sanctity of life" versus "freedom of expression". One's opinion on the situation is going to fall on whichever value a particular person prioritizes. The emotionally-charged, intelligence-insulting lifeboat dilemma you've thrown at me pits a single value against itself - "sanctity of life" (the lives of your family) versus "sanctity of life" (the life of the refugee). You have a choice to hide the refugee or protect your family - but either choice you make, you will be both respecting the "sanctity of life" principle
and disregarding it. That's what makes what you call "the utility calculus" necessary
at all. Since both options both support and violate your principle, it seems to me that the right thing to do is pick the option which is most supportive and least violative of your principle.
How do you do that fairly? First, strip away all of the subjective, emotionally charged baggage words like "Nazi", and "refugee", because those are unimportant. I'll volunteer to ignore the phrase "my family", because I've been raised to understand that your family comes first, since they are the people you already have a foremost responsibility to protect (that might cloud the issue, and again I'm trying to be fair). It finally becomes:
Option 1: Save 6 lives, place 1 in danger
Option 2: Save 1 life, place 6 in danger
There are many ways to "couch" this expression. For example, I can change your problem to
You are endowed with superhuman strength, but not speed. Two out-of-control cars are headed toward a cliff. One contains a family of 6 passengers, one contains only a single passenger who happens to be a prominent womens' rights leader. Each car is assured to roll off the cliff and die unless you save it - however, you only have time to save one of the cars, and you have no alternative options. Which one do you save?
Again, either choice involves both saving and sacrificing life. The fact that the six passengers in one car are a family and that the single passenger in the other happens to be famous are unimportant when it comes down to the nitty-gritty. How do you weigh life? What one single life, no matter who it is, justifies the sacrifice of 6? Do you believe the refugee is entitled to special treatment?
So why won't you support surrendering to rapists as well? In my example, confronting the rapist would almost certainly NOT save more people than it might hurt; if anything, it's pretty certain to do the opposite. So according to your logic, you shouldn't do it because it wouldn't be brave, just stupid and reckless. Give me ONE good reason, according to your own logic, as to why you would interfere with the rape.
Because the issue is no longer "sanctity of life" versus "sanctity of life" (in fact, it isn't any value vs.
any value) and therefore what you call the "utility calculus" no longer applies. Assuming no lives are in danger here (not counting mine - remember, situations like this don't factor in personal safety). I have the choice of acting or not acting. If I act and
fail, the result will be the same as if I had not acted; so let us assume that "acting" automatically means "succeeding" (which I'm confident I could do anyway. I'm
very most likely bigger and scarier than the rapist). Not acting means my wife is raped and the rapist probably goes free. Acting means my wife is not raped, and the rapist may still go free, but the probability of being caught is higher because he's injured or captured.
But of course, since you're married, you've sworn to protect your wife anyway, so this situation has nothing to do with "bravery", it's simply "duty". Thus, not acting isn't "cowardice", it's "negligence".
And before we go on, I'd like to suggest you drop this issue, as you cannot approach it objectively. It's very clear, from the moment you indicated that you took personal offense (because of your ancestry) to my
attempt to answer your question fairly, that you can't proceed neutrally here. It was bad enough that you had the nerve,
knowing what you know about your family's past - to give me such a situation and demand that I make a decision; but to then, after I struggle to find an answer, throw in "oh by the way, my family were Jewish refugees and I'm glad they didn't find
you" and use that as a foundation from which to hurl such terrible vitriol and insist that I would betray my friends and let my wife be raped(!), is a truly dirty trick. From the very beginning of our particular exchange you've given me every reason to be personally insulted and to hold you in the same kind of contempt you seem to be throwing at me, but I've tried to remain neutral, and I don't expect you to apologize for your behavior,
because you cannot possibly be objective on this matter any longer. And there are some very touchy subjects which have been discussed on this forum in the past which I have struggled to not participate in because of my own subjectivity regarding them, so this isn't an empty-handed suggestion.