Lord of the Flies by William Golding is set on a tropical, deserted island, and the characters are all English school boys. The reason that is particularly significant is that English school boys certainly know right from wrong and how to be obedient to rules; however, if one were going to break the rules, a deserted island might be the place to do it.
One of the "rules" of society is that people should not kill. Of course this is true about human beings, but it is equally true about animals. People in a civilized society just do no go around killing things, even a school boy who carries a big knife around with him.
Jack is not a pleasant boy. In fact, he is not even a very nice boy. He talks big, bragging about what he is going to do if he ever gets a chance to kill a pig for meat. We take that for what it is, bragging, even though we do see him slashing candlebud bushes with his knife just because he has no use for them. It is true that, if we believe any of the boys will really use a knife to kill, it would be Jack; however, we know something he does not appear to know--killing something is a very serious matter.
When he is exploring the mountain with Simon and Ralph, Jack sure does a lot of talking about killing a pig, and he finally gets his big chance to do it. Of course he does not do the deed. After he fails to act, he makes stutters around and makes excuses. and things are a little uncomfortable between the three of them for a bit. While Jack does not ever actually admit exactly why he did not stab the pig, the other two boys know.
They knew very well why he hadn’t: because of the enormity of the knife descending and cutting into living ﬂesh; because of the unbearable blood.
Jack knows it, too. These are civilized boys, not savages, and stabbing a living thing with a knife is just not part of their lives. The thought of the consequences--terrible death and blood--is just too much and that is what keeps Jack from acting.
Of course, after that Jack does violently stab a tree with his knife, but he does so more out of anger, embarrassment, and bravado than out of any real change of heart. It is not the same, and they all know it. Jack determines that "next time there would be no mercy." This is an ominous foreshadowing of things to come.
So, Jack is not able to kill the pig because killing is not something well bred and civilized people do, even young, impetuous boys. Jack is not hungry enough, desperate enough, or bloodthirsty enough to do it in the first chapter of the novel.
For more analysis on Lord of the Flies, please take a look at the excellent eNotes site linked below.