Q:

Are we taught to try to understand our fears?

On page 13 of Good Questions, Good Answers it says,

The Buddha taught us to try to understand our fears, to lessen our desires and to calmly and courageously accept the things we cannot change.

Is it true that we're taught to try to understand our fears?
Assuming it's true, do you suppose it means nothing more or less than the first noble truth: i.e. that dukkha is fear and vice versa?
Or does it mean something else?
Are there techniques to "understand our fear"?

A:

Yes, we are taught to understand our fear and see where it comes from.
It comes from the projections of our mind.

As fear is based on something that we think may happen in the future, it is clearly a mental process which tries to predict the future - in that sense, the reason of fear is a projection of our mind.
  We can be afraid to fall, but once we are falling, we are afraid to hit the ground, once we hit the ground, we may fear we have a bad injury, once we know we have a bad injury, we may fear the pain and the consequences of not being able to work for some time or become disabled etc. So one could say that fear is always based on something that has not happened yet, and is therefore a fantasy of our mind rather than fact. 

There are some fears which are wholesome:
Hiri and Otappa which are fear of shame and fear of unwholesomeness are called "Guardians of the world":

"Two lucid things, o monks, protect the world: moral shame and moral dread. If these two things were not to protect the world, then one would respect neither one's mother, nor one's mother's sister, nor one's brother's wife, nor one's teacher's wife ...." (A. II, 7).

There is another fear which results from the practice of vipassana as pointed out by eudoxus:
Knowledge of fear - bhaya-nana

This gives way to the knowledge of fear, (bhaya-nana). In the disappearance of everything examined, the mind at some level begins to realise: there is nothing beneath this parade of changes. There is no foundation. At a fundamental level, there is nothing at all. The result is existential anxiety. In its strong form this can manifest as panic. In its weak form, it can be merely a sense of existential unease, a sense of nothing going right, a sense of helplessness, a sense of loss of control. At this stage of the practice, the meditator’s insight into anatta, not self, usually takes the form of a sense of loss of control. The realisation that "I am not in control of ‘my’ life".

