A man who was present at the creation of Catholic dogma, a presbyter of the Alexandrian church, Arius, opposed that dogma and the political power brokers who crafted it. Catholics have used the term "Arian" as a general appellation for anyone who disagrees with them. When Portuguese Catholics interacted with Ethiopian Catholics during the sixteenth century, the Ethiopians branded the Portuguese as "Arian." Arius eventually recanted his opposition to the troika of Alexandrian Catholic dogma, but it did not prevent him from meeting a violent death. This pattern repeats in history with recanting heretics going up in flames. Recanting was rarely a path to evade the death penalty for thought crimes.
One way to characterize the Arian heresy is that it disagrees with the idea that there is only one True Church. It is open to alternative ideas and alternative personalities outside of the formal power structure of apostolic succession. It recognizes the fallibility of those who passed on the teachings of Jesus. The Church is a political construct that attempted to usurp a prior trademark with its own branding method. It professes the "religion of Jesus" as it practices a cult of power.
Another aspect of the Arian heresy is the idea that we all have the capacity to pursue eternal knowledge. This is the area that has consigned more heretics to the fate of the pyre than any other. Any and all public exposure of the truth about nature or the human condition has been viciously attacked by the Church. It is one thing for a monk or a scholar to know the truth, but it is heretical for them to teach it to others. The laity must be kept safe from reality lest they wander from the fold.
The reason the Arian heresy persists is not because there are evil, scheming, ambitious people like Arius who are out to destroy the Church. The political ambition of the Church is the ultimate driving force behind the heresy. Were it not for the corrupt dependency of episcopal opulence on the deception of the laity, ascetics would never venture to expose people to an alternative path toward understanding. The darkness of deception and delusion causes the heresy to persist in bringing bits of light into the world. The Church has only itself to blame for the Arian heresy.