I put myself into the shoes of a person who might never have given much thought to the potential disintegration of society. One of the questions that such a person might ask is:
If the Rule of Threes implies that the fastest ways to die are to be stupid (three seconds), lose oxygen or blood (three minutes), exposure (three hours), dehydration (three days)...then why is so much more attention paid to food-security which might take three weeks (to three months) to result in death?
Three answers
1.) If the threat is across-the-board and everybody is exposed to it, the number of people who are close enough to your supply to be a threat to you is proportional to the amount of time the victims have before losing consciousness.
How many people could learn about and raid your pantry in three weeks? How many could figure out that you have a wood-stove and break-into your house in three hours? In the case of thirst, how many streams and puddles would a goblin have to walk past before they helped themselves to your supply?
2.) Dehydration and hypothermia result in lethargy and numbing of senses before death. In contrast, hunger makes people more observant. Most notably, hunger increases our ability to smell things by at least ten-fold. Hunger makes people smarter. Hunger makes them more aggressive right up until they slip into a coma. Hunger makes most people dangerous.
3.) Producing food is seasonal and there are very long lag-times.
Assuming you already have a garden-tools-and-seeds, you might be able to harvest radishes and turnip-greens 28 days after planting the seeds, snap-peas, green beans and cucumbers 55 days, early potatoes and sweet corn at 70 days and so-on. Main-season crops, the heavy-lifters in terms of calorie production, might run 100 days.
If you buy a ewe that has been bred, you are looking at one-year before you have a fat lamb to slaughter. If you bought a bred-heifer, you are looking at 2-1/2 years before you have young beef.
If you bought chicks, then you have to feed them human-quality food for four months before you have a snowball's chance of getting eggs. This is different from sheep and cows because they can eat food that humans cannot eat...grass, twigs, standing hay (i.e., the dried grass in that vacant lot or abandoned field) so they are not directly competing with humans for food.
Small-fruits are relatively fast. Everbearing strawberries will produce the summer you plant them. Other small fruits will produce modest amounts in the early years as the bush fills out its allotted space, but you should be getting full crops in three years.
Tree fruits and nuts CAN produce in two or four years but that is for intensive and expensive systems. More traditional, free-standing orchards are in the three-year to ten-year time horizon.
In contrast, harvesting rainwater can be as simple as running the downspout from your gutters into a barrel. Unless you have Chernobyl level pollution, boiling or filtering will give you potable water shortly after your first rainfall. Or, you can risk temporary diarrhea and drink it straight out of the barrel.
Those are the reasons why people who do not wish to become refugees seem to focus overly-much on food security: High external threats and long lead-times relative to how long it takes to starve to death.
Bonus link
Greenhouses in Michigan's Upper Peninsula destroyed by heavy snowfall and winds. Hat-tip to Coyote Ken.
