Ali's view is that Islam is fundamentally a religion of violence and subjugation and that this is the natural interpretation of particular passages in the Quran and hadith literature. She believes that extremists provide a compelling and inspiring case arguing from the Quran and that this is the main reason why they find ready and devout followers. For her, the only viable solution is for an Islamic reformation to occur where such passages are fully repudiated. Without this, a political and authoritarian Islam will continue to threaten the world.
Nawaz makes the case that Islam is not intrinsically a religion of either violence or peace. Rather, there are competing interpretations that promote political violence and social discrimination on the one hand and liberal and democratic ideals on the other hand. What is important is to support people who are looking to reform the discourse and open up the debate in Muslim countries. He also points out the widespread problem of half-truth narratives. This occurs when religious texts or world events are cherry-picked to create false or misleading perceptions. For example, many Muslims think that Americans are anti-Muslim because certain events are played up in the Muslim world (e.g., the burning of copies of the Quran in Florida or the US president claiming that God told him to invade Iraq). Conversely, many westerners learn about the concepts of jihad or sharia from extremist sources and assume that these are the commonly-held interpretations of Muslims.
Rauf makes a different case again that Islam is fundamentally a religion of peace with its roots in the Abrahamic faith. His view is that Islamic jurisprudence has a venerable tradition, often exemplifying religious tolerance, progressive views for women, and intellectual achievement. He notes that Islamic fundamentalism is a relatively recent phenomenon that is discontinuous with the tradition of Islam, particularly with its insistence on an exclusive Islamic nation state which he sees as an incoherent concept. He also sees the need to change the cultural discourse around Islam. Instead of portraying terrorism and fundamentalism as an Islam versus the West battle, to rather understand it as a religious moderate versus religious extremism battle.
One point that especially struck me during this discussion is the problem of half-truth narratives. It's almost always possible to interpret events and textual sources in ways that support conflicting narratives. The real challenge is to form the most likely conclusions from the data that is available. In this case, the two narratives are "Islam versus the West", which Ali argues for and "Extremists versus Moderates", which Nawaz and Rauf argue for.
