Privacy is, at its root, a form of deprivation. The word private comes from Latin prīvātus — the past participle of prīvāre, meaning 'to deprive' or 'to separate'. Something private has been separated from the public. Someone private has withdrawn from communal life.
The Latin root prīvus meant 'individual' or 'single' — standing apart. Roman citizens who held no public office were called prīvātī: private persons, men deprived of official authority. The word carried no shame; it described a state of withdrawal, not defeat.
English borrowed the word through Old French privé, which added warmth: privé meant 'intimate, familiar, personal'. A privy council was an intimate advisory group. A privy (the toilet) was a private place. The modern English privy preserves this older, warmer sense.
The military rank of private appeared in the 16th century. A private soldier served without rank or command — a man deprived of authority, serving in an individual capacity.
The word's most surprising relative is privilege. Latin prīvilēgium combined prīvus ('individual') with lēx ('law') to mean a law that applied to one person only. A privilege was originally a private law — an exemption carved out for an individual. The modern sense of unearned advantage grew from that legal seed.