It was a simple opening question that Emma Alberici's Lateline guest, Islamic radical Wassim Doureihi, would not answer, but there was one other question the ABC host wished she could have asked.

Alberici was at loggerheads with Doureihi, of the group Hizb ut-Tahrir, when he blatantly dodged her line of questions on Wednesday night about the tactics of Islamic State extremists.

At one point, the Lateline host asked: "Are you outraged by the image of an Australian-born child of seven-years-old holding up severed heads like trophies in Iraq or Syria?"

Mr Doureihi replied: "Let me tell you what I am outraged by," before an angry Alberici admonished him for avoiding the question, which went on to become the theme of the night.