The thing the kids at Battle School have largely forgotten is that they are in training for a real war. So many of them are so wrapped up in the "games" and battles against other armies, that they have lost sight of the big picture. Ender realizes that Bonzo is one such student.
Rather than attempting to become the best commander he can be, to learn from others and learn from his mistakes, Bonzo instead takes everything personally. Bonzo has made a personal enemy out of Ender. Ender realizes this - but rather than retaliate, or become afraid, he weighs his options. He knows that the teachers are aware of everything in the school - and at this point he has a pretty good idea that they are not going to intervene in advance to stop something potentially dangerous.
Ender sets his sights on personal survival in more ways than one. He takes personal defense classes in case it ever comes to hand-to-hand fighting with Bonzo. But more than that, he begins to think about how he can be the very best student that ever existed in the history of the Battle School. Ender knows this is his only real chance at not only surviving through training, but surviving the bigger picture as well. The teachers have complete control of Ender while he is in Battle School - and in this chapter he realizes he does not need to worry about petty battles with other students - but instead learn how to beat the system.
The adults are the enemies because they are the ones manipulating the children through the use of these 'battle games', causing the children to fight and battle amongst themselves when the adults were the real ones controlling these games. Through this manipulation, we can see what Orson Scott Card illustrated with his adult versus child relationship.
That's from the prespective of the children. Ender was thinking in terms of "which child is my enemy?" because the adults orquestrated things so that the children would fight each other. Once he recognizes that, even though some children would still behave as enemies, he began to reengineer his thinking to take further into account adults' preponderant roll.