Why would you taunt someone holding a loaded rifle?

Macho, and not too smart. I don't think he had any other way of operating.
I am also wondering whether, if he had been alone with Pyle, he might have tried to talk him down. But he isn't. Joker is there and Hartman has to save face and maintain that tough attitude to the end. Hartman goes out the way he lived - a bad-ass, and not too bright.

"Chicken soup - with a *beep* straw."

He bet Pyle was bluffing and lost the bet.

I have two friends who served, one Army, one Marines, and there was a suicide in both's company. One guy put an M-16 in his mouth and the other was last seen alive taking apart his load bearing gear, eventually using the belt to hang himself.

Luckily neither took anyone with him like in the flick but I'm sure real DIs are faced with situations like this. I think if this was real life and not a movie Hartman would have tried to calm him down even w Joker there.

It seems that Hartman didn't know how to handle a situation like that. He was used to being in charge, shouting insults and bullying the recruits into submission. But this situation called for a softer approach and that was something Hartman wasn't very good at. Joker had more common sense; calling him by his proper name "Leonard" instead of his recruit nickname probably saved Joker from being shot too.