Why do you have to add eggs one at a time, or add liquid and dry ingredients alternately in baking?

--Mark & Nancy

Many cake and cookie recipes start by creaming together a solid fat, usually butter, and sugar.  After this they say to add the required number of eggs one at a time, incorporating each one before the next is added.  Then, the dry ingredients and other liquid ingredients are blended in, alternating dry and wet ingredients.   This is probably the most common procedure in home baking.

If you add the eggs one at a time and blend each of them in well, the fat will emulsify with the eggs, similar to making mayonnaise, only in this case you are adding the eggs to the fat rather than the other way around. 

And just like making mayonnaise, if you were to dump all of the eggs into the bowl at once and try to beat them together, it is much harder, if not impossible to get a smooth result.  Try that some time, and you may have the butter turn into grains that don't blend in.  This isn't fatal to making a cake, but could result in some larger pockets of fat that melt during cooking creating an uneven texture in the finished product.  Also, according to Shirley Corriher in BakeWise: The Hows and Whys of Successful Baking with Over 200 Magnificent Recipes if you over-beat the batter once the eggs are added, you may get a hard, shiny crust on top of your baking that separates from the rest of the food.  This is because the eggs have been beaten to a partial meringue.  If you add all of the eggs at once, you may blend the batter too long trying to get it smooth, resulting in this crust effect.

Once the eggs are incorporated, the instructions say to add some of the dry ingredients, which have already been blended together in a separate bowl, and then some of the other liquid ingredients.  Usually they say to alternate one third of the dry ingredients, one third of the liquid, and so on.  Sometimes it is by halves.

In baking, you want to avoid as much as possible the formation of gluten, which result from the combination of certain wheat flour proteins with water.  Because gluten is elastic, and because chemical leaveners are not very strong, any gluten that is formed will inhibit the rise of the baked product.  Gluten in cookies will make them tough and leathery.  Gluten is desirable in bread making, but not baking.

If you follow the typical instructions to alternate dry and wet, the first batch of dry ingredients you add gets coated with the fat, both from the butter or other fat, and the fat in the egg yolks.  The fat interferes with the formation of gluten.  From there you want to add liquids and dry ingredients mixing as little as possible while still getting everything evenly blended.  Too much mixing will cause more gluten to form, resulting in a denser, more bread-like loaf. 

If you dumped all of the dry ingredients in at once, the batter at that point would be very stiff and may be lumpy.  In an effort to get a smooth batter, you will likely mix enough to form lots of gluten.  On the other hand, if you added all of the liquid ingredients first, you wouldn't get the benefit of the fat interfering with gluten formation.  The balance is found in between, neither adding all of the dry ingredients first nor adding all of the wet ingredients first, but rather in alternating them according to the recipe.