용기를 꺼내다 is VERY off. I never heard it even once. 내다 = to extract (kind of); to make 꺼내다 = to pull; to take out Aren't you mistaken with "용기를 내어 말을 꺼내다"? And yes, that one is fully valid and even quite common. It means "to bring up [sometthing] by plucking up courage".