Fear is a powerful emotion that can cause people to behave badly. Fear of the unknown caused the Puritans to believe in witchcraft and led to the destruction of many lives. This is an example of allowing fear to overtake your whole being, so that a person will do anything he/she has to in order to quit being afraid. On the other hand, I don't believe admitting that you're afraid is bad as long as you don't allow it to control you.
Fear can be a positive motivating factor as well. I have a senior student who had slacked off at the beginning of the semester. His grades fell greatly, and he was told he might not graduate. His fear of not graduating with his classmates and of disappointing his parents motivated him to do extra assignments, to come to school every day, and to get his homework in on time.
I don't know if you've been reading or listening to the news about the fifteen-year-old girl from Ireland who committed suicide due to bullying, but I think this is a perfect example of how fear can have a positive and a negative effect. I believe people who bully others are cowards who are afraid of being picked on or embarrassed themselves. They allow their fears to cause negative results. Those who are being harassed are also afraid to have to deal with the bullying on a daily basis. Their fear, rightfully so, becomes the motivating factor in their lives. The young, Irish girl's fear of being further harassed resulted in her death. Hopefully, however, something positive will come from this situation. It has brought the situation of bullying in our schools to the forefront, and now something can be done to make schools, parents, and students more responsible.
FDR used this phrase to positively motivate American society to remain hopeful instead of giving up. If we become too afraid, we then allow others to control us, and we no longer have control of our own lives. FDR wanted to inspire Americans to respond to a bad situation by doing something positive and not allowing their fears to keep them from reacting at all.