Kreese had just learned that his girlfriend back home had died - a secret his captain had been keeping from him - and the news, plus the fight, caused Kreese to snap and kill someone without any just cause. Not only did this crucible give birth to the Cobra Kai name, but it also showed Kreese to be a man pushed over the edge when he straight-up murdered his captain over the snake pit after it was clear that they were all about to be rescued. It was here that the crazed and toxic John Kreese that we know from The Karate Kid was born. Blaming himself for their predicament, Kreese watched as his friends were made, in pairs, to fight to the death over a snake pit. Sadly, Kreese's hesitation to kill his own friend led to his squad getting captured and held prisoner by the enemy.
In the Army, while serving overseas in the Vietnam War, Kreese was trained in karate and in the merciless ways of warfare and covert ops by his captain.
His mother's tragic suicide led him into a hard life of being picked on and ostracized, which in turn led him into the Army. Throughout Season 3, viewers were given John Kreese's backstory.