I can understand perfectly well when people WANT to sit together, be it because they want to chat, work on a project, plan their trip, like each others company or whatever. To many it is certainly comforting not to be alone in a situation that to them could seem somehow uncomfortable or even frightening. I don't mind a friendly request for a favor at all and will likely grant the favor if it has no substantial disadvantages for me or anyone else (e.g. if through my decision to change seats my former cute, young seat neighbor has a gross guy sitting next to her, I would certainly not want her to have to endure that - she'll be better off with me

).
But I don't understand to what great length some will go to get their way. In these cases the desire to sit together has become a need, as in neediness, dependency or insecurity. Often that goes along with an entitlement attitude.
On booking separate seats (aisle and window with center in the middle), I recognize that it is sometimes a successful strategy to end up with a free center seat.
Somewhat old-fashioned etiquette would give us a few pointers how the arrangement should be handled between a gentleman and a lady traveling together. First, the lady gets the seat she wants. If she wants the center seat, so be it, same for other seats. Second, if possible, the gentleman would then take a seat that allows for her to be shielded from other passengers, especially men. This is of course not entirely unselfishly chivalrous.

So if the lady books an aisle, the man should in principle book the center. This will guarantee that there is no one else directly next to her.
The same applies for visits to the movie theatre or a real theatre/concert/opera. When you have two adjacent seats, which you can switch among yourselves easily, the gentleman will propose that his lady sit next to another lady rather than next to another man while seating himself next to another lady. Several obvious reasons: Assure that the other man doesn't hit on your woman, show that the only lady you want to sit next to is your own lady, avoid any potential jealousy from the companion of the lady you'd sit next to, give his lady more breathing room by placing her next to another lady.
Needless to say, these considerations are often trumped by assuring that the lady has a good view of the stage. If placing her next to another lady would mean that she sits behind a 7ft dude with a top-hat, she will certainly prefer to sit next to a man and behind a shorter person.
Old-fashioned considerations perhaps, but they have always been very well received whenever I had the honor of female companionship for a cultural event.
If somebody ever asked me to move to an inferior seat, I'd politely decline and even tell them why, so next time they know the implications of such a question (which they might have not know this time).
I once had someone poach my seat (he was seated there when I arrived), and I was already starting to be not happy. Well, he was very friendly and gave me his boarding pass for a business class seat. Nice free upgrade for me.

And smart of him, because his lady certainly was pretty enough that I would have been delighted to be her seat neighbor.
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