Trivia: John Woo fought to keep the slash in the title, so moviegoers wouldn't think it was a film about hockey.
Trivia: One of John Woo's directing styles is to mark large action sequences with doves. You can see this in Mission: Impossible 2, on the island just before the final action sequence and in the church after the funeral in Face/Off.
Trivia: The prison that Pollux is in is called Erehwon which is "no where" backwards.
Trivia: One contributor was stationed at George AFB near Victorville, CA where the airport scenes were filmed. The base closed in '92. Here's something if you really want to get technical - they fight inside a hangar and then to the hush house (engine testing area where Cage is blown into the wall by the engine afterburner). It looked as though they went through the hangar straight to the hush house. He worked in both of these buildings and had to either drive to the hush house or walk very far across the flight line. Looks good in the movie, unless you were there...
Trivia: The names Castor and Pollux Troy are taken from the constellation Gemini. In Roman mythology the Gemini which is Latin for "twins", Castor and Pollux, are the twin sons of Leda and the brothers of Helen of Troy and Clytemnestra. According to the myth the twins had the same mother, but different fathers. While Pollux was immortal, Castor was mortal. When Castor died, Pollux asked Zeus to keep them together and so they were transformed into the Gemini constellation.
Trivia: The magnetic boots worn by all the inmates in the sea prison are the same boots worn by the Goombas in "Super Mario Bros."
Trivia: As an example to the contrast of their characters, Sean Archer's blood type is said to be Type O and Castor Troy's is said to be AB. Type O is the universal donor type and Type AB is the universal recipient type.
Chosen answer: Although they were on the same side, Troy is currently posing as Archer, which means he would have to do everything that the FBI would expect Archer to be doing. The whole point of the raid was to take out Archer, as well as Troy's gang. He would have rather risked killing part of his own gang than risk exposing his identity to anyone else.
Casual Person
That doesn't really make sense. In the scene, he goes out of his way to shoot him and smiles while doing so, carefully and slowly. Was not a collateral damage situation. The question is why he deliberately goes out of his way to kill him.