I graduated from mechanical engineering, and even though I really don't use any of the equations and stuff anymore, it's surprising how often the basics show up in everyday life, like drywall.
Your presumption that thin drywall would break when bent doesn't fly from an engineering point of view because paper is actually quite strong in tension. Try rolling a piece of paper up into a tight roll and pulling it apart and you'll discover how strong it is in tension.
It's exactly that property of paper that makes drywall rigid. You see, for drywall to bend, then the paper on one side or the other has to stretch to accomodate that change in shape. The thinner the drywall, the less the paper has to stretch to accomodate the same change in shape, so thinner drywall bends easier than thicker drywall.
It's the same thing with steel rebar in concrete. When concrete is properly reinforced with steel re-bar, the rebar is typically placed on both sides of the concrete, just under it's surface. The purpose in doing that is to keep the concrete rigid. With steel rebar inside the concrete on both sides, then the steel rebar on one side or the other of the concrete slab has to stretch before the concrete slab will bend.
Lots of times you'll see a single layer of steel rebar in the middle of the thin concrete slab, like a floor or sidewalk, for example. In that case, the purpose of the rebar is not to reinforce the concrete to make it stronger and more resistant to bending; it's only to hold it together in one piece. That single layer of steel rebar would not strengthen the concrete at all, it would only help hold it together in one piece if and when it breaks. If instead you put a layer of rebar like that on both sides of the slab, then the slab is very much more difficult to break because it has to bend before it breaks, and the steel rebar on one side or the other has to stretch before the slab bends. The result is a slab of concrete that is very much more difficult to bend, and therefore seems to be "stronger", even though the concrete itself isn't any stronger.