Superficially, I am sure there are lots of answers for why an American citizen might decide to affiliate with ISIS and become a terrorist. But I think deep down, at the foundational level, there is a common trait for Westerners who turn toward radical Islam. In a world that tells them nothing creates everything, no one has a purpose, and there is nothing after the grave save rot and worms, the tiny voice instilled in all mankind cries out that there is more and these Westerners have gone on a misguided search for what that more is.
In the neo-pagan world of western society, in the beginning was nothing and nothing created the heavens and the earth. Nothing said, "Let there be light," and from nothing flowed a big bang of energy from which all matter was created through random chance.
Nothing then through a random collision of atoms created apes that evolved into mankind in heterosexual and homosexual form, with something created out of the nothing allowing each person to decide on their own maleness and femaleness.
At the end, each person will die after years of leaving a large carbon footprint helping destroy the earth. Their bodies will decay in the ground, the worms will eat them, the trees will feed on their nutrients, and over time all will be forgotten. Eventually the sun will expand, consume the earth, and the very existence of all people will be stamped out as the universe slowly darkens. There is no purpose except avoiding pain and maximizing pleasure.
The secular lefts of the West are neo-pagans and this is their cosmogony and eschatology. It is a falsehood built on a flight from God who calls out for us to have a relationship with him. God is reflected in nature. "His invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made." (Romans 1:20)
Some people become restless confronted by this neo-pagan nihilism. They ask what came before the big bang and are either scoffed at for asking a nonsensical question, or they get a nonsensical answer. Maybe it is multi-verses or universes ad infinitum. Essentially, the neo-pagan theory of creation amounts to turtles all the way down.
These restless souls hear the voice in the back of their head telling them that there is more, there is something greater, and they were meant for eternity. Rejecting the veneers of a rotting western culture, those from Islamic backgrounds go seeking their higher purpose in their heritage. They swing as far toward their native culture as the secular left has swung away from traditional western culture. There they find radical Islam and it answers the call of the voice in their head.
Instead of Christ calling to love and repentance to get to eternity, radical Islam calls for jihad and promises eternal glory. Where they see nihilism in the West, in the East they see purpose, passion, cause and glory.
The neo-pagan West, filled with a secular cult of death just as pernicious as Islam, but wrapped up in compassion and choice instead of conquest and caliphate, cannot calm the cry of the voice in the silence. One death cult provides no answers for another. Only the compassionate call of the Christ who yearns for an eternal relationship with us can do so. But the death cult of the secular west with assisted suicide and abortion will side with the death cult of Islam and its suicide bombers and executioners because the things of this world hate the things of God and creation has declared itself creator. Therefore Christianity can be scapegoated so no one need answer tough questions.
Why do American citizens become terrorists? Because they know the neo-pagans premise the world on a lie, but they get lost in their quest for the truth.