I dont understand why the crew member was trying to plead with the lady to switch meals...sounds horrendously unprofessional!!!! Now if this lady was an unpaid upgrade, a staff passenger or something to that effect then yes change her meal but dont do what that steward was doing! That sounds awful!
It happens all the time. In BA we can have up to 70 passengers and 5 meal choices. Usually a Beef of which there is probably about a 60% loading, a chicken of about 20%, something veg and something light of about 10% and 5% and then a couple of cold main course salads. The company along with all their other money scrimping have reduced the over flow loading so narrowly now that the chances of not getting what you want are much higher.
I personally (although we are told not to do it) when taking the meal order usually take the orders based on FFP rank starting with gold cards, then silver and so on ending with Upgrades and then staff! That way the most important passengers in the cabin are least likely to be put out!
But its all about diplomacy at the end of the day! At the end of the day you must remember that even the best restaurants can run out of a particular meal half way through the night as demand was perhaps misjudged!