Captain Miller in Saving Private Ryan (1998) orders the assault on the machinegun nest because he was embarassed by his conduct in the previous scene (explanation in the comments)

Rule 5:

In the film *Saving Private Ryan* (1998), Captain Miller (played by Tom Hanks) orders a frontal assault on a machinegun nest which results in the tragic and completely unnecessary death of the squad’s medic. This decision was indefensible, and his subordinates repeatedly urged him not to take it. They were only one squad, it was unrelated to their objective, and they could have easily bypassed the gun. Quite frankly, it’s a miracle they didn’t all die in the assault. Miller argued that they had to take the position to prevent a theoretically greater tragedy should an entire company of infantry (for context: a company is about 200 men) blindly walk into it, which was unlikely. And should that happen, a company has the necessary firepower to brush it aside easily.

In the scene just prior, the squad arrived at an airborne field hospital and began combing through dog tags of KIA airbone infantrymen for the name of the man they were sent to rescue. As they search, the men make a game of it **in full view of an airborne unit marching past them making light of their dead comrades**. Worse, Captain Miller is standing among them, quietly partaking in the grim little game they were playing. The squad medic, who was tending to the wounded, sees this happening and runs over to break up the game, chastizing them. Miller looks around with a sense of profound embarrassment at his own conduct. After they got a clue as to where to look for Private James Ryan, Miller pulls his men aside to map their route. The squad goes silent as Miller notices the compass shaking uncontrollably in his hand.

I argue that the real reason Miller assaulted the machinegun nest had nothing to do with his aggression or mentality about casualties, but about regaining confidence in himself and his men. This was a fatal miscalculation, and it nearly causes the group to fragment, murder a POW, and commit fratricide.