Because “dirt” aka “soil” is composed of both inorganic material (like the silica in sand) and decomposed organic material (carbon, nitrogen, etc).
In order to build soil, you need adequate moisture and nutrients for plants to grow, die (or drop leaves), and be broken down by decomposers (insects, bacteria, and fungi), and you need some kind of root structure or a layer of humus to hold the soil in place and prevent its being eroded away by wind and water.
You don’t have those things in a desert. Not enough water for significant plant growth, not enough organic nutrients in a purely mineral sand, and nothing to prevent the desert wind from blowing away any soil that does form.
Deserts can be sand, clay, and probably some other things. The dirt you’re thinking of is the same but with a lot of dead stuff in it like leaves, grass, etc. That stuff just doesn’t grow enough in the desert to make dirt. So the sand is in a lot of places all over the world. It just looks like the dirt you’re talking about.
There are two things at play here: size sorting by wind, and lack of organic material in the soil. Fundamentally, this comes down to lack of water (and therefore also plants).
First off, what is sand? It’s a particular _size_ of rock particle. Bigger than dust and clay, smaller than gravel. Sand can blow around a little bit in the wind, but not too much.
Second, what is soil? It’s a mix of organic material and rocks of all sizes, from clay to sand to gravel. The exact proportions vary from place to place.
> rest of the world lacks sand.
That brings us to this part of your question. The rest of the world _doesn’t_ lack sand. It’s got lots of sand, just mixed in with the other components of the soil.
So what happens when you have an area with normal soil and it becomes a desert. First, the ground dries out and the plants mostly die. The soil is no longer held in place by roots or moisture. This is where the wind comes in.
Wind blows across this dry, loose soil, and the surface organic material and clay-sized particles tend to blow away out of the desert entirely. The organic material also breaks down, and it’s not being replaced because of the lack of plants.
So what’s left behind? Sand, gravel, rocks. And this is your typical desert, which is actually more rocky than sandy. It’s a [desert pavement](https://en.wikipedia.org/wiki/Desert_pavement), a layer of small rocks and gravel left behind covering the surface of the desert, and trapping the material below and keeping it from eroding.
But what about the sand? It’s not quite small enough to blow away entirely, but it is small enough to be moved around by wind. If the geology is right, it can get concentrated into certain parts of the desert, forming your classic desert dunes. But these are actually a fairly small part of the overall desert.
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