Why are there four Sunni schools of law?

Answer

They are the four early legal traditions — Ḥanafī, Mālikī, Shāfiʿī and Ḥanbalī — whose methods of deriving rulings from Quran and Sunnah were preserved and taught in an unbroken chain. Their differences concern method and evidence weighting, not the foundations of belief.

Source: Classical fiqh tradition · al-Muwaṭṭaʾ · Kitāb al-Umm