穿 sets a tooth 牙 under the cave radical 穴: gnawing through. To pierce came first; clothing followed — you 'pierce' your head and arms through a garment.
穿 dresses and drills: 穿衣服 (put on clothes — note the logic: clothes are 穿-ed, hats and accessories are 戴-ed, a distinction learners drill), 穿过 (pass through — streets, tunnels, forests). 看穿 is to see through someone's act; 穿越 powers China's beloved time-travel drama genre (穿越剧) — piercing through dynasties for love. Getting dressed and breaking through: one character does both every morning.
A tooth 牙 boring through 穴 — PIERCE through; slip THROUGH your clothes: WEAR.
穿越剧 'pierce-through dramas' — the time-travel romance genre — takes its name from this character's drilling power.