In recent decades, the massification of online social connections has made information globally accessible in a matter of seconds. Unfortunately, this has been accompanied by a dramatic surge in extreme opinions, without a clear solution in sight. Using a model performing probabilistic inference in large-scale loopy graphs through exchange of messages between nodes, we show how circularity in the social graph directly leads to radicalization and the polarization of opinions. We demonstrate that these detrimental effects could be avoided if the correlations between incoming messages could be decreased. This approach is based on an extension of Belief Propagation (BP) named Circular Belief Propagation (CBP) that can be trained to drastically improve inference within a cyclic graph. CBP was benchmarked using data from Facebook and Twitter. This approach could inspire new methods for preventing the viral spreading and amplification of misinformation online, improving the capacity of social networks to share knowledge globally without resorting to censorship.