It is not known whether Pavlo Hummel is deliberately holding on to the grenade and allowing it to explode or not. He is more likely, as he later explains to his projected alter ego Ardell, planning on throwing it back out the window but is unable to do so in time. Whatever the case, the reason Pavlo grabbed the grenade in the first place is right in the title of the play: it was his "basic training."
Because of his answer to Ardell's question as to why Pavlo did what he did, we can assume that his actions were without any kind of planning or forethought. He has simply been conditioned to act with bravado in even the most absurd and hopeless of circumstances. Ardell says that the circumstances of Pavlo's life and death are "all shit," speaking also to the military's method of taking away autonomy from soldiers during their training.