Before we can deconstruct why mold is so efficient at destroying wood, we first need to understand what makes wood so strong. The wood's grain, its bundles of parallel fibers and tubules that used to carry sap creates a strong internal structure. Like the ripples of a tin roof or a bundle of soda straws, they resist bending and breaking.
Secondly, the chemical structure of its cellular tissue. Wood is made of cellulose fibers that are strong when they are stretched. These are embedded in lignin which is strong when it is compressed and also water-resistant. Molecules of hemicellulose link the lignin molecules together for even greater strength.
Breaking it down
Unlike your typical green plants, fungi are not capable of photosynthesis. They need a ready-made source of energy, and also water. They produce enzymes (proteins that make chemical reactions happen) and excrete them into their surroundings to break down dead organisms for the energy and building materials they need.
Cellulose is a large crystalline molecule made of many hundreds of glucose molecules linked together, hemicellulose is a large molecule made of various 5-carbon sugars linked together, and lignin made of 6-carbon atoms in rings linked together in a large maze of carbons and oxygens and hydrogens.
It may sound strange, but wood is made of carbs. Energy-rich carbohydrates waiting to be consumed. To humans it's inedible, but to wood rotting fungus, it's a banquet. Wood rot fungi produce enzymes to break cellulose into glucose that can be absorbed by the fungus. Other enzymes can turn hemicellulose into small sugar molecules. Lignin is a bit more difficult chemically, but a few fungi produce enzymes that can break down lignin and convert it into sugars.
Wood rot is simply what happens to wood when a fungus has it for lunch. Removing any part of the mix of cellulose, lignin and hemicellulose from the structure degrades the integrity of the wood. It may merely become soft and "punky" or be completely converted into strands of fungus cells.
The cellulose in the paper cover of drywall may be attacked by mold, but drywall destruction is mostly from water. The strength of drywall comes from layers of paper and glue laminating a brittle compressed plaster-like core of gypsum. The gypsum reacts with water and chemically combines with it. It loses physical strength and puffs up a bit.
Keep it dry, keep it strong
Unless you built the structure in a semiconductor clean room, the spores of wood rot fungi are there, waiting for water so they can start growing. Without water, fungi can't produce enzymes. No enzymes means the wood structure stays intact.
No wood repair will be effective unless the source of the water that allowed the fungus to grow has been located and stopped.