I was taught (by an ex-RAF instructor who had flown in WWII) that it was for 'sucking in' and to call out 'sucking in' before swinging the prop (with the fuel turned on but the mags off).
With all due respect to your instructor, whom I've likely never met, I flew radial powered airplanes utilizing R-1340's, R-2600's, R-2800's, R-3350's, and R-4360's, and have a little bit of an idea of radial engine operation...not from listening to someone else, but from having done it as a professional pilot in the cockpit, as well as years of working on that equipment as a mechanic. The information I previously relayed to you is correct.