Golding shows us mankind's dark side. But why doesn't he present a solution?
Yes - it's interesting isn't it. luannw has given you a good overview on Golding's theory of the "blackness within", and the "darkness of man's heart". But I think there's also a political dimension to this question:
Here's a quote from William Golding:
The theme (of Lord of the Flies) is an attempt to trace the defects of society back to the defects of human nature. The moral is that the shape of society must depend on the ethical nature of the individual and not on any political system however apparently logical or respectable.
The argument Golding is making that it is a society full of good individuals that becomes a good society. That you can't impose goodness through rules. You have to foster it from within. And the society in which "Lord of the Flies" is located is set in a war - the plane is "shot down", and at the end, its a naval officer who rescues. The sort of behaviour in the book, Golding argues, is what a society at war breeds.
So the structures of the civilisation in which the novel is set are at fault. And within that, the boys' behaviour - being seduced by the glamour of a mask, a hunt, and persecution of others, particularly with a tyrannous leader like Jack - is strongly reminiscient of the behaviour of many countries during World War II and the rise of Nazism. Our structures, Golding argues, are clearly not trouble-proof, clearly not darkness-proof.
But more interestingly, Golding seems to be arguing that any structure (however apparently logical or respectable) is wrong, is a bad thing. Society should depend on the ethics of an individual, not on a group policy or ideology.
So maybe that is the solution. Individuals forming societies based on their own ethics. It's a complicated one: wouldn't that be an anarchy - everyone doing their own thing? Where does a sadist like Roger fit into that? What about the vulnerable members of society (the littluns)?
But that, I think, is what Golding is arguing.
Golding doesn't show us the much of the good side of mankind because he felt there wasn't much of a good side. Golding believed that mankind was flawed; that all people had an evilness within them that they kept hidden because of the rules of living in a society and because it served their purpose to keep it hidden so they could continue to live and thrive in society. Jack's manipulation of the boys, promising them, in chapter 9, to have freedom from worrying about the beast, to have food, and to have fun, is an example of how Jack kept his beast temporarily hidden so that he could appeal to the boys. When he beats one of the littluns shortly after, for no reason, he has again let out his evilness. When Golding does present some goodness, such as in Simon who discovered the truth about the parachutist and the real source of evil or such as in Piggy, who understood the necessity of being responsible and of thinking, he has those spots of good killed. He felt that was what mankind did - they killed off the good because the evil inside was greater and more powerful than the good. Much of Golding's view came from his service in the British Navy during World War II. He witnessed man's inhumanity to man and it colored his opinion of mankind. He felt all people were capable of evil and this book tries to establish that view point.