Bread most often crumbles when sliced because it is cut right after coming out of the oven, before its internal structure has had time to settle. The starch inside hot bread is still partway through gelling, and as steam escapes, the bonds holding the crumb together have not fully set yet.
What makes crumbling worse?
A dull knife is a major factor too; a knife without serration, or a blunt one, compresses and tears the bread instead of cutting it cleanly, scattering crumbs everywhere. The direction of the cut matters as well; pressing straight down instead of using a gentle back-and-forth sawing motion increases crumbling.
Dough that was not kneaded enough is another cause; if the gluten network has not developed enough, the bread's internal structure stays weak and falls apart easily when sliced, even once baked. Bread that has gone too dry or stale has a similar effect; as it loses moisture, it loses the structure that holds the crumb together.
What gives clean slices?
Letting the bread rest for at least 30 to 45 minutes after baking, or a few hours for large loaves, until it has cooled completely, gives the internal structure the time it needs to settle. That waiting period is the most basic step toward whole, even slices.
Using a serrated bread knife and cutting with a sawing motion instead of pressing down hard also cuts crumbling significantly. Checking the knife's sharpness regularly serves the same purpose.
Kneading the dough for as long as the recipe calls for lets the gluten network develop fully, helping the bread stay in one piece when sliced. A well-developed gluten network is really the skeleton that holds the baked bread's crumb together.
How the bread is stored also affects how well it slices; bread kept in an airtight container or bag holds onto its moisture much longer and crumbles far less when cut than bread left out uncovered.
The bread's internal structure affects how much it crumbles too; large, irregular-holed, crusty breads like baguettes fall apart more easily when sliced than tight, fine-crumbed sandwich bread, because the thin walls between the holes are more fragile. That is why two different types of bread can give very different results even when cut with the same care.
The cutting surface makes a small difference too; bread can slip slightly on a smooth surface while being cut, throwing off the knife's path and increasing crumbling. Using a slightly textured, stable cutting board helps keep the bread in place and gives a cleaner cut.
Interestingly, keeping bread in the fridge does not slow staling, it speeds it up; the starch's re-crystallisation, known as retrogradation, actually happens faster at fridge temperature than at room temperature. That is why bread is best kept at room temperature in the short term and sliced and frozen for longer storage.