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.
Colon cancer. Colonoscopy is performed to detect early colon cancer, it is recommended at age 50 and then at 10 year intervals for average risk. If there is a personal or family history of colon cancer it might be recommended to start earlier or more often. General surgeons and gastroenterologists are the two specialties that perform colonoscopies.
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.