Why does sunrise times move slower than sunset times?

They don't really, when you calculate the values for the entire year. It only SEEMS that way, in the weeks following the winter solstice in the northern hemisphere. Part of that is because the Earth is in an elliptical orbit around the Sun, and reaches its perihelion (the closest point to the Sun) around January 4 each year. On that day, the Earth is moving fastest in its orbit around the Sun.

If you look at the location of the Sun in the sky at the same time every day for a year, you'll see that the Sun appears to make a figure-8 shaped pattern in the sky. This is called the "analemma"; you may have seen it printed on some globes.