Halogens like $\ce{Cl}$ always exhibit $+7,+5,+3,+1,-1$ as their oxidation numbers. I found the following answer after checking several sources:
Halogen atoms have $7$ electrons in their valence shell, so $1$ of those electrons is spin unpaired, which is an unstable situation. If an even number oxidation occurs, said even number of electrons are taken away, leaving still an odd number of electrons with at least $1$ unpaired. Taking away an odd number of electrons leaves an even number of electrons with the opportunity of them to be all paired.
These oxidation numbers are observed in compounds like $\ce{HClO4}$ and $\ce{HClO3}$. We know that, before forming these compounds, the valence electrons of $\ce{Cl}$ are excited into the d orbitals. Thus now, they are not in ground state, but in the excited state instead.
The quoted explanation is giving the reason for my question on the basis of the ground state of halogens. (I especially consider $\ce{Cl}$). But we know that, before formation of compounds, the halogen atoms are in their excited state instead.
So is the quoted explanation correctly justifying why $\ce{Cl}$ exhibits odd oxidation states only?