Why would my family doctor send me to a general surgeon to have a colonoscopy?

Preference. He probably prefers the surgeon to do this over a gastroenterologist. We can do colonoscopy it is just most surgeons don't do it.
Screening. Surgeons are also trained in endoscopy. Some surgeons perform their own endoscopies because then at the time of the operation they know exactly where to operate.
Not sure. The standard of care is for a gastroenterologist or colon and rectal surgeon to perform the colonoscopy, but many general surgeons are also trained and proficient in performing a colonoscopy.