A popular
machismo sentiment - If you show you're
bleeding, you show you're weakening
physically, and thus weakened
psychologically, the enemy smells
blood, and then - you're finished, and you can't win the
fight you
had to win.
Lets have some history to this : "Never Let Them See You Bleed" was paraphrased and adopted as a working maxim for a soldier in the British Army whilst the uniform was still a redcoat. Why the Redcoats? One of the main reasons, other than tradition, was because it was thought that the enemy officer would find it harder to calculate the fighting status of their men if they couldn't tell which ones were stabbed/shot and bleeding (red life juice) profusely. Secondly, the fighting men themselves, in their awkwardly buttoned down redcoats, would find it hard to see if they were bleeding and would probably fight on - assuming of course that they felt no pain, as often happens after shock.
Hollywood uses it to great effect, for example, when the hero gets wounded in a very painful and mildly life threatening way (i.e. if he doesn't get medical attention real soon) the hero of the movie cannot show himself bleeding to the innocents he's trying to save. He must show a brave, invincible front so that the hostages/victims will have complete faith in him being able to rescue them and escape, and the bad guys will think he's mechanistic killing machine on two legs. When/If the hero of the movie does show his pain and blood to another, usually to his romantic interest, he will instinctively reject being tended to and soothed, because that would be to show weakness.
(And of course anasthetic is totally out of the question godamnit! He might have a broken neck and be pierced by two or three bullets in a surprisingly fleshy part of the chest, but he needs his wits at 100%, his senses can't be numbed if he's the only one who can kill all 500 of the rebel/terrorists and land the one-winged plane!)
Although into today's real world this stiff upper lip psychology isn't literally applicable (er...usually!), it makes for a great metaphor in the killer emotional situations of life, and may explain why some people are so instinctively afraid to donate blood.