This is just definitional, isn’t it?
This is like asking “why does ten thousand 1-gram weights weigh 10 kilograms?” Molar mass is the mass of 1 mol (a quantity) of an element, and the atomic mass is that divided by the quantity. Replace the word “mol” with “million” (it’s not 1 million, but it helps you see the tautology).
Rewritten this way the question asks: “why does an atom have the same mass as 1 millionth of a million atoms?”
The atomic mass is *defined* as “the molar mass, divided by the number of atoms in a mol”
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