Which quotes from Lord of the Flies best illustrate the theme that evil is inherent in everyone?
I would highlight the chant that the choir boys yell while on the hunt:
"'Kill the pig! Cut his throat! Kill the pig! Bash him in!'"
Combined with Ralph's observations when finally faced with the pig itself:
"The desire to squeeze and hurt was over-mastering."
And, finally, any description associated with Roger, the most evil of the boys:
Roger stooped, picked up a stone, aimed, and threw it at Henry— threw it to miss. The stone, that token of preposterous time, bounded five yards to Henry's right and fell in the water. Roger gathered a handful of stones and began to throw them. Yet there was a space round Henry, perhaps six yards in diameter, into which he dare not throw. Here, invisible yet strong, was the taboo of the old life. Round the squatting child was the protection of parents and school and policemen and the law. Roger's arm was conditioned by a civilization that knew nothing of him and was in ruins.
Some of the best quotes that illustrate evil is inherent in everyone come from Simon. In Chapter 5, when the boys are arguing about the beast, Simon says, "Maybe the beast is us", indicating that Simon under the truth that the beast (evil) is inside each one of us. During Simon's hallucination, the beast says, "I am a part of you," Golding seems to imply that no matter what name you give to evil, be it sin, the devil,neurosis, hate, violence, terrorism, or sheer wanton destruction, these traits are inside of man. This idea is confirmed when Simon discovers the beast truly is a man in the form of a downed parachutist. When he tries to bring the truth to the rest of the boys, they kill Simon in a frenzy--pointing to Simon and saying "Kill the beast"!
In order to select quotes which illustrate the theme 'evil is inherent in everyone' it is important to refer to the context of the quotation as much as the words themselves. The final chapter, where 'Ralph wept for the end of innocence' should be reflected on to consider whether the boys ever were innocent, or just ignorant at the start. Ralph, by the end of the novel, has begun to understand the evil found 'in the darkness of man's heart'. Of course the quotation refers to mankind, but it should be noted that technically none of the major characters are men. We have seen evil committed in the story--cruelty, betrayal, murder--and yet what could be most chilling is that these are the crimes of children: the last vestige of goodness. This would clearly illustrate that 'evil is inherent in everyone'.
I agree with the above poster that the dialogue between Simon and Lord of the Flies is a good start. You might also have a look at the moments of the two deaths - Simon's and Piggy's: particularly the way that even the good characters like Ralph are drawn into complicity with the murderous tribal behaviour. For Ralph, remember, in the hunts, "the desire to squeeze and hurt was overmastering".
You might also have a look at the moments of the hunts and compare the communal mentality of sadism (as embodied best by Roger: "Right up her a**e") here to that at the two murders.
And don't forget that hugely important last page - look at why Ralph cries: "the darkness of man's heart".
The dialogue between Simon and the Lord of the Flies would be a good place to start. The Lord of the Flies taunts Simon with the idea that there is no escaping him, and, if we see him as the symbol for mankind's inherent evil, then this means that Simon learns he cannot escape his own inner evil. He then leaves to warn the others that this is what they must all fear, not some imagined beast.
Acting on his darker impulses, at first in small ways, he knocks over Percival and Johnny's sand castles. Then he throws stones at Henry, only missing because his arm "was conditioned by a civilization that knew nothing of him and was in ruins."
"They corner the wounded pig, and when she falls they are on her. Roger is particularly cruel, driving in his spear slowly by leaning his weight upon it until the sow screams in agony."
"Roger shows no mercy. He and the boys laugh at the screaming pig. They become hysterical after seeing where Roger had twisted his spear while inside the anus of the pig."
"Numb to the sufferings of others, he releases the rock that knocks Piggy to his death and tortures the twins into submission."
"He prepares a stick, with points sharpened at each end, on which to mount Ralph’s head."
One especially good quote is from ch. 7 was "The desire to squeeze and hurt was overmasting". This showed that even though they were raised as civilized boys their is a beast within all of them