Here's another way of explaining it.
F-number is focal length divided by the diameter of the aperture (in fact the entrance pupil, but let's ignore that for now). A 105 mm f/2.8 lens has an aperture of 105/2.8 = 37.5 mm diameter.
As you focus more closely, a simple lens would have to move further away from the sensor/film. At 1:1 a simple lens would be twice as far from the sensor/film as it would be when focused at infinity. At infinity the simple lens would be one focal length from the sensor/film. At 1:1 the simple lens will be two focal lengths from the sensor/film - ie 210 mm in this case.
The f-number is now 210/37.5 = 5.6.
Because your Micro-Nikkor is cleverly designed, it achieves f/4.8 at 1:1 instead of f/5.6.
Best,
Helen