Run your fingers across a piece of silk so fine that you cannot feel the individual threads. That is the original meaning of subtle. Latin subtīlis meant 'finely woven' — from sub ('under, below') and tēla ('a web, a warp'). Something subtīlis was woven so tightly that the threads passed beneath the threshold of perception.
The metaphor extended naturally. A subtle argument has threads so fine you cannot see them until the conclusion tightens around you. A subtle flavour is one that works below the surface of your palate. A subtle person operates beneath your notice.
The word entered English via Old French sotil, and for two centuries the spelling matched the pronunciation perfectly. Then came the Renaissance. Scholars, determined to honour Latin etymology, pushed the b back into the spelling to match subtīlis. English speakers, equally determined, refused to pronounce it. The silent b in subtle has been a monument to this standoff ever since.
The Latin root tēla connects subtle to an unexpected family. Text, textile, and texture all come from Latin texere ('to weave'). A text is something woven from words. A textile is something woven from thread. And something subtle is something woven so finely that the craft becomes invisible — the highest compliment to any weaver, writer, or strategist.