I'm going to agree with Szczerzo about this being an anthropologic question, but I'm going to disagree about the cause.
While nomadic lifestyles was an influence, it's not causative.
I'm also going to ignore the distinction made about raising agents in the OP, because it's factually incorrect; most Arab/Levantine/Turkish/Kurdish breads use yeast.
Instead, I'm going to answer the distinction between loaf bread and flatbread.
Specifically: loaf bread is an aberration, not flatbread.
You find flatbreads around the world in every society that has access to any kind of grain anywhere.
Europe, Asia, Africa, Americas, Malaysia, everywhere.
Some are raised (yeasted) and some are not.
Some are filled and some are not.
All grains are used: wheat, barley, millet, rice, lentils, corn, etc.
Whereas:
loaf bread pretty much only shows up in Egypt (and nearby) and in Europe, and there's good reason to believe that the latter two regions learned it from Egypt.
Thing is, loaf bread requires several different things to be easily and cheaply available in the same place: Wheat or barley (high-gluten flours) Ability to build brick, stone, or earthen ovens
(this is where nomadism isn't compatible) Ability to cultivate starters (both the right grains and the right weather) Inexpensive, but hot, fuel for ovens (e.g. wood)
This combination simply didn't happen in too many places; either people lacked suitable grains, lacked cheap fuel, didn't build ovens, or simply never got started (the Babylonians appear to only have made flatbread, for example, despite having all the right ingredients and tools).
So it's really not so much a question of "why did X culture only make flatbread" as "why did these three places make loaf bread?"
If you're interested in this, I highly recommend the book Six Thousand Years Of Bread .
cooking.stackexchange.com/users/7180/FuzzyChef
It's actually an anthropologic question.
It's more due to
Europe being settled down while Middle Eastern peoples were still nomadic.
Raising bread, even with agents, is very hard when you move or don't have much time.
For a raised bread you need a starter and few hours; for a flat bread you need a few minutes.
Not to mention flat bread can be baked ON an oven or grill while you cook other food alongside within minutes (it takes me around 10 minutes to prepare 20 flats) while European bread needs its own oven and around 1 hour to make.
cooking.stackexchange.com/users/47855/SZCZERZO KŁY
It's also worth mentioning that many flatbreads have a rather long storage life.
For instance, the Sardinian pane carasau is split and cooked a second time so that it could be used on months long trips.
It's quite possible that the different climates and jobs led to differences in bread making.
cooking.stackexchange.com/users/67/Joe
Perhaps the difference is not so much between leavened and unleavened as between flat and loaf.
In colder climates, there is an existing need for a persistent fire, which has been lit for heating, as well as cooking.
In those cultures, ovens and baking are more likely to arise.
Even the leavened breads of the Middle East and South Asia tend to be flat, and more quickly cooked.
Given a persistent fire and an oven, loaf breads have the advantage of economy of scale.
More weight of them can be produced, without the need for constant attendance, in larger simultaneous batches, than of flat breads.
cooking.stackexchange.com/users/59328/Robin Betts
As @Marcin stated in the comments above, there are no sources for the answers given, and many of the answers have issues:
Materials , it may not be the prairie, but wheat, spelt, barley, and rye were all available and used for breads even in the ancient Middle East Resources , sure, there's less wood for ovens and flatbread cooks more quickly, but desert temperatures are higher, ovens hold heat more efficiently, and the Middle East had plenty of ovens and kilns.
Not only that, but plenty of things other than wood burn, having fire in the freezing night temperatures of the desert is essential, and nomadic desert folk still keep campfires going and cook food.
Lifestyle , yeah, lots of nomads, herders and the like, but like @Marcin stated, cities existed.
Not only that, but cities tend to be cultural centers as well.
We tend to define a people's cuisine and culture by what large centers of life do, not by their more sparse and scattered population.
Shelf Life , c'mon, if anything, the dry Middle East is going to have a longer shelf life for goods than all the moisture up north.
But, all that is unsourced speculative rebuttal.
If I had to pick a reason, it's yeast.
Even in Europe, when you look at the fairly well-documented history of beer and wine ( http://www.thecomicbookstoryofbeer.com ), people relied on wild yeasts.
The microscopic world wasn't a concept and yeast was obtained by luck mixed with trial-and-error.
Wild yeasts may be more abundant in the moist, plant-rich environment in Europe; they are spread in the air and in the foliage.
While some Middle Eastern beer was made from fermented bread, it is possible that much of the yeast for beer and wine may have come from imports.
While beers and wines were made in the Middle East, yeast from one batch is used to make the next (even today, wherever they are made).
Unlike in spirits, in breads much of the yeast dies in the baking.
How much more convenient it must be to mix together some flour and water, maybe some oil and salt, throw it on a sheet of metal that's been sitting in the sun or over your campfire, and watch it turn into a pita.
cooking.stackexchange.com/users/67870/undrline
Tandoor style ovens commonly used in the Middle East and Central Asia where you cook the dough sticking it to the walls only work with flatbreads.
The process of leavening Uzbek non, for example, is similar to most Western loafs but it is flattened with a bread stamp right before going into the oven.
I don't think the lack of fuel is the reason since there places with thick woods but still baking flatbreads (The Caucasus or the Southern shore of the Caspian Sea.)
cooking.stackexchange.com/users/67965/Rodrigo Varela Tabuyo
This may be a history question so please move it if appropriate.   Culturally, local ingredients dominate cooking recipes and national dishes (e.g., soy in SE Asia), but why do Europeans add a raising agent to bread items to make  loaf bread  whilst people from the Middle East still favour flat breads?  Were raising agents discovered in Europe and never migrated?  Is there a taste difference?
Why did flatbread dominate the Middle East but Europe adopted raised breads?
cooking.stackexchange.com
<bread><history><leavening><flatbread>
cooking.stackexchange.com/questions/90638
cooking.stackexchange.com/users/32621/Venture2099
The reason is unlikely to be fuel, but rather differences in climate, rising time and ovens. Flatbread rises quickly, can be cooked on an oven or grill or on the walls of a tandoor while other foods are being cooked, is ready in minutes and has a longer shelf life. Flat bread is found in more areas of the world than loaf bread. It is easier to make and requires less time. Loaf bread requires a raising agent and time to rise. Moreover, some ovens are not designed for cooking loaf bread. Flat bread generally stays fresh longer.
Flatbreads are found everywhere. Maybe jobs and climate led to different ways of making bread. Raising agent is important in loaf bread. Flat breads can be baked on any fire and the typical ovens in the Middle East are only designed to cook flat bread. Flat bread keeps fresh for longer. Lack of fuel was not a reason for the different bread making style developing in different areas.