A pure compression structure is a pool of liquid. If you add some shear strength, so the structure can withstand compression and shear but no tension, you can additionally build a heap of sand or a pyramid with no internal voids. To build a vertical wall, much less an arch or vault or nonuniformly-drying adobe†, your material needs to withstand some tension—a property you only really come to appreciate after attempting to build or plaster with adobe containing too little clay or too little straw‡, then watching the structure crumble as it dries.
It's common to analyze masonry structures as "pure compression structures", but that's a useful simplification permitted by considering the bricks to be atomic units. The tensile stress trying to peel the bottom surface off a brick arch is small, but it's real, and if not resisted by the tensile strength of the brick, the arch collapses from the inside out, like the sand arches that sometimes form above an aperture in a moving-sand-picture desk toy. Fired-clay bricks have enough tensile strength that we don't have to think about this, but adobe is just at the limit where safe and reliable building is possible with enough care. For this reason, traditional adobe walls are very strictly vertical, but their surfaces are not; they are significantly thinner at the top than at the base.
(I'm not an architect or structural engineer, but I spent much of my childhood in adobe structures, I've taken a few adobe-construction classes, and in the process I've built a few adobe structures that are still standing.)
______
† Nonuniformly-drying adobe is not a particular type of adobe. It's the nature of the drying process that, during drying, the surface of the brick or wall is dryer than the core—it's precisely that moisture gradient that causes moisture to diffuse out of the core, thus allowing the core to dry. But that same moisture gradient sets up a tensile stress in the surface, which you can diminish but not eliminate by adjusting the adobe mix. Even portland-cement concrete does this, though to a smaller extent.
‡ Straw or other high-performance, fibre-reinforced stabilising agents, of course.
