Before paper there was silk: documents were written on silk scraps, and the earliest paper was pulped from silk rags and plant fiber. The silk radical 纟 in 纸 remembers that lineage — paper is silk's cheaper descendant.
Cai Lun's 105 AD refinement of papermaking is one of the Four Great Inventions (四大发明). Paper stayed a Chinese secret for six centuries until captured papermakers carried it west after the Battle of Talas — arguably history's most consequential leak.
Silk 纟 for the common clan 氏 — PAPER, everyone's silk.
纸老虎 'paper tiger' — fierce-looking, easily torn — entered global vocabulary through Mao's 1946 interview and never left.