One is not born a terrorist but becomes one.
One is not born an insurgent or a resistant but becomes one.
And yes, plenty of the current ones were not terrorizing before the US invaded Iraq.
Some like Zarqawi come from abroad (he's a Jordanian and I don't think King Abdullah of Jordan is our enemy); but most of what you call terrorists were not terrorizing their own people (Saddam was there to prevent anything outside of his control) before the US invaded Iraq.
When a country is being invaded and occupied by a foreign power, the latter sends to the population a signal as strong as one coming from a rapist to its victim.

Of course, their natural feeling is to defend their country, their culture, their history and who they are. And they become dangerous because they are motivated, much more than the invader who's wondering what he's doing there anyway.

Raoul