Diamond asks: Why did agriculture never arise independently in some fertile and highly suitable areas? Why, among the areas where agriculture did arise independently, did it develop much earlier in some than in others? Two possible explanations are propose: there's either a problem with the apples (plants are not domesticable) or a problem with the Indians (people were sucky).
The fertile crescent appears to have been the earliest site for a whole string of developments including cities, writing, empires, and civilisation. The advantages of the fertile crescent include:
(1) It lies within a zone of so-called Mediterranean climate, characterised by mild, wet winters & long, hot, dry summers. The climate is important because it selects the plant species that are able to survive the long dry season and resume growth rapidly upon the return of the rains. Plants there are annuals that dry up and dies during the dry season. One year of life produces big seeds instead of making inedible wood/fibrous stems such as trees and bushes. They constitute 6 of the modern world's 12 major crops.
(2) Wild ancestors of many founder crops were already abundant and highly productive, occurring in large strands whose value must have been obvious to hunter-gatherers. These crops made it easy for hunter-gatherers to collect huge quantities of wild cereals when the seeds are ripe for storage and enables them to settle down more permanently even before plant cultivation. Such ease of domestication—as compared to other crops such as corn that had to undergo drastic changes to become useful—made it the among the first crops to develop in certain areas, including the Fertile Crescent. This contrast between wheat/barley (big-seeded annuals) and the difficulties posed by teosinte may have been a significant factor in the differing developments of New World and Eurasian human societies.
(3) Flora included a high percentage of hermaphroditic selfers which meant that their reproductive biology was convenient for early farmers. Furthermore, on the occasions that they did cross-pollinate, they also generated new varieties among which to select from. Of the first significant 8 crops to have been domesticated, all were selfers.
Th question that turns to why, if they had the same climate, did other zones in the Mediterranean fail to rival the Fertile Crescent as an early site of food production? What advantages did the Fertile Crescent enjoy?
(1) Has the world's largest zone of Mediterranean climate. A larger area meant a higher diversity of domesticable plants.
(2) Greatest climate variation from season to season and year to year, which favoured evolution among the flora, especially in a high percentage of annual plants. The combination of high diversity & high percentage of annuals with large seeds means a high diversity of annuals.
(3) It provides a wide range of altitudes and topographies within a short distance, which means that harvest seasons can be staggered. Hunter-gatherers could thus harvest grain seeds as they matured instead of being overwhelmed by a concentrated harvest at a single altitude.
(4) Wealth in ancestors—because they have a lot of diversity over a small distance—not only of valuable crops, but also of domesticated big mammals. The early domesticated animals (goat, sheep, pig, cow, horse) lived in sufficiently close proximity that they could be readily transferred after domestication from one part of the Fertile Crescent to another, such that the region had all four species. Agriculture could arise in the Fertile Crescent from the domestication of locally available wild plants without having to wait for the arrival of crops derived from plants domesticated elsewhere. So agriculture was launched in the fertile crescent by the early domestication of 8 "founder crops" — 3 cereals, 4 pulses, and flax. The fertile crescent thus had an advanced biological package for intensive food productionction*.
(5) It may have faced less competition from H/G lifestyle than that in some other areas because mammal species hunted for meat are overexploited by the growing human population and reduced significantly, the food production package quickly became superior, hence there was a quick transition.
In the other areas, the problem does not lie with the people as well.  Ethnobiological studies have shown that hunter-gatherers know all their locally available wild species and their crops. And  they do exploit their knowledge to domesticate the most useful available species as evidenced by studies that demonstrate that the hunter-gatherers of the time brought home only the most useful available seed plants and avoided toxic plants or those with small or unpalatable seeds.
New Guinea offers a contrast to the fertile crescent because their indigenous food production was restricted  by the local absence of domesticable cereals, pulses, and animals,  by the resulting protein deficiency in the highlands, and  by limitations of the locally available root crops at high elevations. This is despite knowing as much about the wild plants and animals as people today. Thus, New Guinea is the perfect example of Diamond's stance that limitations on food production has nothing to do with the peoples, and everything to do with the biota and environment. Especially since when local peoples promptly took advantage of productive crops when they arrived from elsewhere*, and increased greatly in population.