Along the lines of what @oratio said, it is because the problem is far more complex than it might seem. The most glaring difficulty of which I am aware is that, even though wealthy nations may easily produce enough food to feed the rest of the world, to distribute this food freely would be to destroy the livelihoods of farmers in recipient areas; those farmers could continue to survive on handouts, but they would lose their capital. Since impoverished nations are generally dependent on agriculture, this would essentially reduce them to passive dependents, and would prevent them from building viable economies in the future. The people would be saved in the short run, but the structure of society would be devastated for generations to come. Far better, therefore, to help local farmers, with loans of capital, tools, animals, seed, equipment, etc., to be able to feed themselves and to produce a salable surplus, and to develop surrounding areas to allow them to better reach the people who need to buy their food. Those people must in turn be given jobs at fair wages so that they can afford that food, or in a pinch subsidies can be used to lower prices, which requires industrial development and the fostering of international fair trade.
All of this, however, is exceedingly difficult. In large part, this is due to the greed of corporations which have an interest in squashing that industrial development and free trade, and of banks that are unwilling to lend to small farmers on fair terms. But a very significant factor is that the poorest regions are often the most volatile. It is a vicious cycle; when people suffer, they seek immediate relief, and they can find that relief in crime: piracy, banditry, drug and arms trafficking….Naturally, these activities destabilize the region and make it almost impossible to create a self-sustaining economy; and so, the region gets poorer, and more people turn to crime. Humanitarian efforts must therefore wait for the slow grind of politics to forge stability from this mess, while the political efforts rely in turn on humanitarians to reduce the suffering that threatens stability; a constructive loop, if you will, that must try to wear down the destructive loop of suffering and instability. As you can see, this is a delicate and slow process, much complicated by ideologies, cultural differences and political blunders, no doubt on top of innumerable factors of which I am ignorant.
So that is why we have not ended world hunger. Give a man a fish, feed him for a day, teach a man to fish, feed him for the rest of his life; but you have to make sure that his boat isn’t going to be commandeered by a paramilitary group, that the trawler downstream isn’t going to depopulate the reservoir, that the price of fish isn’t going to plummet to the point that he would rather buy someone else’s fish, sell his rod, and be unable to fish later…the world’s a complicated place, yo.