This is totally wrong, women are afraid of c-sections and many c-sections start as natural births and go until the baby begins to falter. In fact, many women choose to have natural birth second child AFTER having a child via c-section even though natural birth after a c-section (VBAC) is very high risk for mom.

Women who are "afraid" of natural birth will get an epidural to help mitigate the pain, not a c-section.