We present comprehensive evidence quantifying the magnitude and scope of false polarization (i.e. the impression that opinions on political issues are more polarized than they actually are) on social media, driven by users' selective posting behavior. Using more than a decade of social media behavior connected to individual ideological attitudes in 1.7 million posts, a series of controlled experiments, and a large global survey covering 40 countries (total N = 49,222), we find that (1) strong ideologues post their opinions significantly more often than moderate individuals, and (2) extreme attitudes are posted more often than moderate attitudes. This general pattern replicates robustly across 40 countries, spanning diverse political cultures. Indeed, across studies we find extreme opinions are overrepresented on social media by at least 6% and up to 22% compared to their true prevalence in our samples. Furthermore, the opinions that users post are more hostile and toxic than the beliefs they keep to themselves. These results were not explained by political interest or consistent left-right differences, suggesting that political extremity has an independent effect on social media behavior. Thus, most of the observed polarization of online discourse in recent years may be attributable to the systematic over-representation of pre-existing extreme political views, rather than the causal effects of platforms.