Why is the mass number approximately, but not exactly equal to, the mass of an atom in amu?

because it is all relative to carbon12, there is nothing special about carbon. It was just chosen as the measure unit to base all units on, as all units are slightly different.
The approximate has to do with it being measured with its weighted average of its isotope.
This average is weighted by the abundance of that isotope.
In the following formula we have the weight x by the abundance of the isotope to give the final number, which is in approximation to carbon 12.


mg 24 23.9850amu x .7899 = 18.85
mg 25 24.9858 amu x .1000 = 2.499
mg 26 25.9826 amu x .1101 = 2.861 amu
total: 24.31