HONG KONG—Government authorities had hoped that the unrest and upheaval of the past few months would recede after youthful protesters returned to school on Monday. Thousands of students proved them wrong by boycotting class.

Students at dozens of high schools across the city participated in protests, dressing in black or uniforms, carrying placards and forming human chains outside schools as a new term began. At the alma mater of Carrie Lam, the city’s chief executive, secondary school students held signs saying, “Chief Executive:...