Since fight/flight behaviour is regulated by the amygdala and basal ganglia, you can say:
Anxiety stems from our amygdalae getting started up, because they sense a threat where none is, and effecting inappropriate behaviour thereafter.
Actually, the threat is often correctly sensed, it's just the behaviour (running away, attacking, feigning death/freezing) that's not useful in the modern world.
The therapeutically interesting question is how to change that.
Compared to the rational parts, those emotional mechanisms are much deeper and better wired to the rest of the brain. At the same time they aren't very sophisticated. Some people refer to them as "reptilian complex".
We can't adjust emotions directly and in general we have to wait much more time (think: weeks, sometimes months) to let new ideas like not being afraid of something sink into the subconscious.
But knowing and accepting that makes it possible to grow.