You are wrong if you think that immediately, the day after winter solstice (Dec. 21st) the sun starts to set later and rise earlier. The truth is in Cheyenne, Wyoming, the sunset started setting later each day beginning around December 12th, after bottoming out at 4:30 pm it is already getting later each day. Conversely, the sunrise doesn’t start rising earlier until around January 8th, after hitting the latest sunrise of the winter at 7:24 am. Don’t believe us? Visit any number of sunrise/sunset calculators.
While it is true that Dec. 21st is the shortest day of the year, it is an average and marks our furthest away position from the sun.