What's the problem with that part exactly? He's showing the method which most airlines use, which is boarding by boarding class, The algorithm that they use is

What's the problem with that part exactly? He's showing the method which most airlines use, which is boarding by boarding class, The algorithm that they use is not ordering person by person, there's going to be randomness with who gets into line first, which is what allows for the lack of optimality. The whole point is that the current approach doesn't allow ordering person by person.