Why the Earliest Sunset Comes Before the Shortest Day
The evenings turn first
The shortest day is Dec 21, everywhere in the US. But the earliest sunset is not. In New York, NY it comes on Dec 8, at 4:28 pm, and the latest standard-time sunrise does not come until Jan 4, at 7:20 am. So by the solstice the evenings are already a little lighter, while the mornings keep getting darker into January.
Why it happens
Clocks run on an average day of exactly 24 hours. The real solar day, noon to noon, is about 30 seconds longer than that in December, because Earth is near the closest point of its orbit and moving fastest, and because of the tilt of its axis. So solar noon slides later on the clock by about half a minute a day. Day length is barely changing around the solstice, so that slide wins: sunset drifts later and sunrise drifts later too.
How far apart the two dates are
The gap depends on latitude. The farther south, the more the slide dominates, because day length changes even less there. Across this dataset it runs from 3 days in Fairbanks, AK, where the earliest sunset is Dec 18, to 25 days in Honolulu, HI, where it is Nov 26.
What it means in practice
If the dark drive home is what bothers you, the worst is over around the second week of December, not at Christmas. If it is dark mornings, the worst is early January, which is when a sunrise alarm clock earns its keep. Every place page lists both dates for that town, and the earliest and latest sunsets guide shows where in the country the evenings get darkest.