Question

the size of cation is always smaller than that of its parent atom justify

Answer 1

Cation is an ion which have positive charge on the parent nuclei. Since protons(+) are bound to nucleus so no more protons can be added.
But electron revolve around nucleus in respective shells. So we can bring + charge by removing electrons.
So cation will always have less electrons than parent atom.
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Answer 2

The size of an atom decreases if the nuclear charge ( positive charge ) increases. The increase in positive charge increases the nuclear force of attraction. Since in a cation , number of electrons is less than protons, the nucleus will attract the electrons more tightly because the nucleus which attracts the electrons in a neutral atom can attract the less number of electrons more effectively. Therefore the size of a cation overall decreases and its size becomes less than the parent atom.