Why are cations smaller and anions larger in radii than their parent atom?
The size of the parent atom is measured in terms of the radius of the valence electron(s).
To become a cation, one of the valence electrons must be removed. The shielding effect between like (electronic) charges is relieved, and the positive nuclear core contracts the ionic radii with respect to the atom.
On the other hand, if an atom is reduced, an electron is added to the valence shell. The valence shell should expand to accommodate electron-electron repulsions and thus an anion should be inherently larger than its neutral parent atom.
As a chemist, as a physical scientist, you should look at some data to see whether these assertions are valid. Here is a start.