Ultra-Orthodox male plight: Sitting next to women on planes

There are TSA agents who know my name. I can draw a freehand map of the airport. I have a had a passport that was not valid three months after international travel and was not allowed to board the plane. I have seen a drunk woman who was, in fact, so drunk that she could not get up from her seat. I have not, however, seen an Ultra-Orthodox man ask to switch seats because he was seated next to a woman. That said, I rarely go on flights with Ultra-Orthodox clientele, but every so often, I read a story about "Orthodox seat swapping" in the paper, along with the conflicting opinions that go along with it: it's embarrassing, it's degrading, he did the right/wrong thing, G-D is on his side, etc.
As a fairly observant young Jewish woman, I sympathize with both sides of the argument, but find it difficult to sympathize with and condone public embarrassment. Both parties are probably mortified at the seating arrangement, but only one of them (the Ultra-Orthodox man) embarrasses the other (the woman/traveling companion) in front of the whole plane.
In Judaism (as in many other religions), embarrassing people publicly is a sin-- so much so, in fact, that causing blood to drain from one's face (or rush to one's face) is comparable to murder. (That's what many people say-- no joke.) Being publicly asked to move spots because you are a woman is embarrassing to say the least. (And I say "asked" lightly, because, in many cases, the man actually refuses to speak to the woman.) Now, I understand the man's plight, but there are ways to avoid this problem-- and public shaming is just not one of them.
Frankly, if an Ultra-Orthodox man refused to speak to me on a plane but indirectly asked to change seats and alerted the whole plane as to his problem with my gender (or rather, my not being his wife), I'm not sure I would switch spots. I do not view his seating choice as sexist, just as I don't view being shomer negiah (not touching the opposite gender) or not talking to boys as sexist. It's simply an issue of religious modesty. And I deeply respect that. What I don't respect is how this religious modesty becomes an excuse to embarrass people publicly. I have read accounts of Ultra-Orthodox Jewish men refusing to speak to the women next to them and making it clear to the whole plane that the woman's gender was the problem rather than the lack of modesty. Even if I am sensitive to the request, the way I would be treated in such a situation makes me feel like less than a human being. Again, I understand that Orthodox Jewish men do not talk to women who are not their wives, but to embarrass them by not speaking to these women directly or calling a whole plane's attention to their refusal to sit next to a woman is, in my mind, a greater sin. (Not to mention delaying a flight and stealing others' precious time.)
Some people got so angry after reading about this incident that they suggested throwing the men off the plane-- which is equal embarrassment in a sense, but, on the other hand, may teach the man a lesson to change his ways. As someone suggested to the New York Times, he can just buy two plane tickets.  The reward for handling the situation smoothly is twofold: not touching a woman and not embarrassing a woman. (Or any human being, for that matter.) And as an added bonus, not delaying a flight!
I remember a girl I met who was shomeret negiah. She told me that she would shake hands with a man if he offered his hand so as to protect him from embarrassment. So I encourage all Orthodox Jewish men to follow this fellow human being's example. It is critical not to bring anyone to shame, so the next time you make travel arrangements, keep the red face of your female travel companion in mind and buy two seats.
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