Unless you're on the equator, neither the earliest sunset nor the latest sunrise of the year is on the winter equinox (source). In Pittsburgh, the earliest sunset is usually around December 9 or 10. People who keep Shabbat tend to notice this.
This happens because apparent solar time doesn't line up exactly with mean solar time. The day isn't consistently (or exactly) 24 hours long, and "noon" usually isn't exactly 12:00. Plus there's some shift because of latitude. Fine.
I wondered why there wasn't a corresponding effect at the summer solstice, and played around with this slider to map it out. There actually is an effect, but it's much smaller -- the earliest sunrise was parked at the same time (rounded to the minute) from June 10-19, and the latest sunset is parked at the same time from June 23 - July 1. So in the week or so surrounding the solstice there's barely any change, while in December the boundaries more more visibly. The latest sunset is June 23 which is barely past the solstice, but it's also July 1 (and every day in between of course). And the earliest sunrise is only a couple days before, but also a week before. So what I notice is "earliest sunrise June 19, latest sunset June 23", even though those bands are wider. In the winter, on the other hand, sunset has been creeping later for a week and a half when you get to the solstice.
I guess this, too, is because of latitude, but it's still not intuitive to me. I wonder what's still wrong with my mental modeling.