Origins
Fabric has nothing to do with weaving — at least, not originally. The word descends from Latin faber, meaning 'artisan' or 'craftsman', specifically one who worked in hard materials like metal, stone, or wood. Fabrica was the workshop where such work happened.
The shift from workshop to cloth took centuries. Latin fabrica meant 'the product of skilled work' — anything a craftsman made. Medieval French narrowed this to fabrique, applying it both to buildings and to manufactured textiles. English inherited both senses in the 15th century.
The structural meaning persists in phrases like 'the fabric of society' and 'the fabric of a cathedral'. Architects still speak of a building's fabric meaning its physical structure — walls, roof, foundations. This is the older, more literal sense.
Latin Roots
In most other European languages, the word stayed closer to its Latin origins. Spanish fábrica means 'factory'. Italian fabbrica means the same. German borrowed it as Fabrik. Only English pushed the meaning decisively toward textiles.
Fabricate preserves the craftsman sense most clearly. To fabricate something is to construct it — and when applied to lies, it implies the same deliberate skill that a faber brought to metalwork.