A full explanation of this can be found in the December, 1988 issue of Sky and Telescope magazine on page 674.
If you were to observe the position of the Sun every day at exactly the same local time ( not daylight savings time!) the Sun would trace-out a figure 8 pattern. In the northern hemisphere, this 'analemma' would have a small top loop, and a large lower one because between spring-summer-fall, the Earth moves slowest in its orbit around the Sun than in the fall-winter-spring period when it is approaching perihelion on the Winter Solstice and moving the fastest along its orbit.
Now, the exact bottom of the analemma's winter loop marks the position of the Sun at the Winter Solstice when it arrives at a declination of +23.4 degrees, it's highest northern position due to the tilt of the Earth's axis. But, the problem is that the analemma only stands vertical to the horizon for an observer at the equator of the Earth. Only for observers along the equator will the latest sunrise ( and the earliest sunset) always occur on exactly the Winter Solstice. For all other observers at other latitudes, the analemma is tilted on its side.
Draw a figure eight with a small top loop and a large bottom one, but tilted at, say, 45 degrees to a line drawn through the figure representing an observer's western horizon at a latitude of +45 degrees North latitude.
*A
*
*
* C
*
*
* *
*
*
Western Horizon ...........................................*...........
* *B
*
D
Label A is the Summer Solstice, B is the position of the Sun at the Winter Solstice, and C is the position of the Sun at the Equinoxes. Now, The Sun is at point B on December 22, but look, there is a point D which is still lower in elevation. This means when the Sun reaches point D, it will rise even LATER than it did at the Winter Solstice! On or about January 14, the Sun arrives at this position. A similar phenomenon makes the time of the earliest sunrise occur in early December.
So the answer has to do with both the observers latitude, which causes the analemma figure to be tilted, and changing speed of the Earth in its orbit, which gives the analemma its broad figure-8 shape.