There are over a dozen subcategories of FGM. What you described is Type III, infibulation, where the external clitoris, hood, and labia are removed with the vagina stitched almost shut. This is also the rarest type. Type IV is the most common worldwide -- scraping, incising, piercing. Essentially, fully functional genitals.

Routine circumcision in the US was originally promoted as a way to curb masturbation. If we are to believe that FGM is wrong on the basis that it's meant to suppress female sexual pleasure, the same reasoning can be applied to circumcision, regardless of who is promoting the practice.