I don't know why, but it seems to me that the human eye is interested in contrasts. Somewhere along the way our brains just evolved that way, probably to help us survive better. In any case, the end result is that a big part of what makes any design work is giving it contrasts - contrast in shapes, sizes of shapes, textures, etc.
Contrast in line is one of the most basic design elements - straight lines against curved lines. A drawing that is all straight lines will be stiff. A drawing that is all curved lines will probably look mushy. A drawing with a good balance of curved and straight lines is usually the best solution.
The challenge is how to use straight lines when trying to portray living forms in space. There aren't many real straights in nature. Walt Stanchfield had some good advice about that.
As Walt points out, fleshy forms will turn into straight lines when they come into contact with a flat surface. Also, when two fleshy forms are pressed together (like a woman lowering her arm until it presses into her breast) it creates a straight line where the two forms meet.
Look no further than this Milt drawing to see how straights are played against curves to create a great drawing.
Bruce Timm is a good example of someone who can suggest form and a real figure while using straights vs. curves to get an appealing design.
The more stylized the drawing, of course, the easier it is to exploit the magic of straights and curves.