I understood that better before I read your explanation.
OK, try this. Suppose the ship can accelerate very quickly, and travel so close to the speed of light, that time is dilated by a factor of 6, so that on a 1-year journey (Earth time), only two months elapse on the ship.
The ship goes out on January 1st. The pilot waits until a month elapses, and calculates what the time is on Earth. Only five days have passed; it's January 6th.
Then he slams on the brakes, turns it around, and heads for home, quickly ramping back up to cruising speed. In another month, he'll be back on Earth. He again calculates what the time is on Earth. It's December 26th; only five more days will pass on Earth until he gets there. Happy Boxing Day.