How do you view the arguments presented supporting the relationship between secularism and extremism? What has led to your persuasion or dissuasion? Illustrate your case by presenting exemplars, patterns, and cases in point.

I’m not sure if, from the wording of your question, you’re alluding to the views of a specific writer or statesman about this issue. Ever since the Enlightenment there have been reactions against “secularism” by those who have claimed that without a religious basis, society will descend into chaos. Edmund Burke, in his Reflections on the Revolution in France, wrote what is probably the most seminal treatise advancing this argument. Though in 1790, when he wrote it, the French Revolution had not really turned violent yet, Burke predicted that the abandonment of traditional government and of religious institutions would lead to extremism and would pose an apocalyptic danger to all of Europe.
Those who disagreed with Burke, such as Thomas Paine, were implicitly or openly against both organized religion and monarchical governments. If by “extremism” we include any sort of violence on a mass level, then it’s surely true that the European powers did not need secularism to encourage this. Warfare was the constant state of affairs in Europe when the entire continent was united under Christianity, and became worse after the Protestant Reformation split Europe in two along religious, not secular, lines.
Nevertheless one could assert that after the Enlightenment, when religious belief was weakened, Europe became even more violent. In the twentieth century leaders such as Stalin and Hitler murdered millions of people in cold blood, in a time when both Communists and Fascists certainly were “secular” and held religion in contempt. So as with almost everything there are two sides to this issue and no definitive way of resolving it.