A strict teacher is, at the Latin root, a tight one. Strict comes from strictus, the past participle of stringere — 'to draw tight, to bind, to compress'. The image is of a rope pulled taut: no slack, no give, no room for deviation.
The PIE root *streyg- meant 'to press' or 'to rub', and its Latin descendant stringere generated one of the richest word families in English. String is something drawn tight. Strain is the tension of being pulled. A strait is a passage drawn narrow between two landmasses. Stress is the pressure of being compressed.
Restrict means 'to bind back'. Constrict means 'to bind together'. District comes from Latin districtus — a territory drawn tight under authority, where a magistrate's power was binding.
The most surprising member of the family is prestige. It comes from Latin praestringere — 'to bind the eyes, to dazzle, to blind'. In 17th-century French, prestige meant 'illusion' or 'conjuror's trick'. The modern positive sense of glamour and reputation developed later, but the etymology remembers that prestige was originally a con: something that bound your eyes so you could not see clearly.
Strangle belongs here too — from Greek strangalē ('a halter'), rooted in the same idea of fatal tightness. The family's range, from classroom discipline to murder by compression, shows how far a single root can stretch.