Every Boolean algebra $A$ is isomorphic to a field of set. In particular, if $A$ is finite, then $A$ is isomorphic to the power set of its atoms.
Now, suppose that $A$ is free Boolean algebra with 2 free generators (or atoms). Because $A$ is a finite Boolean algebra, it is isomorphic to the power set of its atoms. However, $A$ has $16$ elements, whereas the power set of its atoms has only 4 elements.
Could anybody explain what I seem to miss.