The phrase "subversive nature" refers to something that aims to overthrow or undermine established systems or beliefs. It implies a tendency to disrupt or challenge established norms or authority. Full definition
Bishop Barron goes on to say that «both Dorothy Day and Mrs. Dawson intuited the properly subversive nature of the way Catholics gather for prayer.» (firstthings.com)
As a reward for making what might be the greatest fiction film about the lives of Chinese citizenry during the Cultural Revolution, The Blue Kite director Tian Zhuangzhuang would be exiled from his country's movie business for nearly a decade due to the supposedly subversive nature of his work. (timeout.com)
He also discusses the somewhat subversive nature of his work, and tells us a bit about what we can expect from the conclusion of book 3. (sciencefictionfantasybooks.net)