Fear is an instinctual response to danger (real or imagined). When the danger is real, fear mobilizes our resources to protect us from harm. And this is a good thing. When fear is associated with insecurity, then we wind up protecting ourselves, not from actual danger, but from fear itself (the "what-ifs"). When this happens, fear morphs into anxiety.
Becoming more courageous doesn't mean you have to become fearless--the courageous person doesn't eliminate fear, he/she manages it.