I suspect part of the explanation is: Part of what manifests as brilliance is early development of the mind. Consequently, brilliant people tend to think, "Well, I was mature enough in my early teens, and surely there must be others like me—perhaps some even younger. The law should not restrict those who are mature enough; that is like restricting adults." The train of thought may continue with something like "There are already mechanisms for having a child make an adult-level decision: parental approval, child emancipation", or "The legal age of consent varies enormously around the world and throughout history, and is clearly arbitrary". (The biologically non-arbitrary age points would seem to be "puberty"—probably around age 12-16 depending on which pubertal milestone you choose—and my 7th grade science teacher's favorite, "when the brain's frontal lobe finishes developing", which would be age 25 or so.)

If the person is also resistant to discarding views merely because those views are hated, then, well, it's easy to see how their beliefs might end up where they do.