The problem lies in the used terminology and the way it was hijacked to denote something other than it's original meaning. Radicalism is unislamic. It is unchristian too.
Just because someone claims to do something in the name of a religion doesn't make it so unless there are explicit instructions in that religion that back those claims. The KKK claimed to be christian yet most christians will tell you that what they did was unchristian. Jihad is an Arabic word that simply means struggle and not Holy war. The prophet of Islam himself called fighting enemies the Lesser Jihad and refered to the day to day challenges of life as the greater Jihad.
This is how terminology is hijacked to manipulate minds and opinions.
Radical Islam doesn't exist. Only radicals who claim or happen to be Muslims. There's your cognitive dissonance right there.