Ender, having beaten Salamander Army against the odds, then shames Bonzo Madrid even further by asking Bean, his youngest Toon leader, to publically announce where Bonzo went wrong and what he should have done to have beaten Ender. This humiliates Bonzo even more than his defeat, which really he knows and recognises he should have won. It is only as Ender leaves the battleroom that he reflects that what he did by using Bean to highlight Salamander's mistake would be taken as a personal slight by Bonzo rather than understood for the attack that it represented against the techers:
Bonzo would only know that he had been defeated even when the odds were stacked in his favour; that Ender had had the youngest child in his army publicly state what Bonzo should have done to win; and that Ender had not even stayed to receive Bonzo's dignified surrender.
Such actions, seen from this perspective, would drive Bonzo's hatred of Ender into murderous rage, which of course is never a good idea, and results in a very close showdown between Ender and Bonzo later on in this novel.