Polarization is a ubiquitous phenomenon in social systems. Empirical studies document substantial evidence for opinion polarization across social media, showing a typical bipolarized pattern devising individuals into two groups with opposite opinions. While coevolving network models have been proposed to understand polarization, existing works cannot generate a stable bipolarized structure. Moreover, a quantitative and comprehensive theoretical framework capturing generic mechanisms governing polarization remains unaddressed. In this Letter, we discover a universal scaling law for opinion distributions, characterized by a set of scaling exponents. These exponents classify social systems into bipolarized and depolarized phases. We find two generic mechanisms governing the polarization dynamics and propose a coevolving framework that counts for opinion dynamics and network evolution simultaneously. Under a few generic assumptions on social interactions, we find a stable bipolarized community structure emerges naturally from the coevolving dynamics. Our theory analytically predicts two-phase transitions across three different polarization phases in line with the empirical observations for the Facebook and blogosphere data sets. Our theory not only accounts for the empirically observed scaling laws but also allows us to predict scaling exponents quantitatively.