Explain why the mole is used as a counting unit for mass

It isn't.  

Explanation:

It is a counting unit for "things" — atoms, molecules, ions, etc. —  and these things all have different masses.

For example, a chemist may know that one atom of Cu reacts with one atom of S to form one molecule of CuS.

Cu + S ⟶ CuS

She knows that 1 mol of Cu (6.022 × 10²³ atoms of Cu) has a mass of 63.55 g and 1 mol of S (6.022 × 10²³ atoms of S) has a mass of 32.06 g.

By measuring  out 63.55 g of Cu and 32.06 g of S, she knows that there are just enough atoms of each element to react with each other.

Thus, the mole has enabled her to count atoms.

the atomic number will stay the same no matter how many electrons it has, so it doesn’t decrease nor increase. it’ll only change with a different number of protons