Why can't O form OF6?
One possible explanation involves atomic size.  You need a large enough atom in the middle to stabilize all the occupied orbitals in the octahedral structure; sulfur makes it but oxygen does not.
This reference gives the molecular orbitals for sulfur hexafluoride.  A key feature of these molecular orbitals is a doubly degenerate pair, labeled $\mathrm{2e_g}$ in the above source, which effectively contains the &quot;extra&quot; valence electrons in fluorine-based orbitals.
The picture below, taken from a different source due to limited downloading options from the free one, includes one of these combinations (here labeled $\mathrm{3e_g}$, as different nomenclature is used) among others.

If we look carefully we see that the ostensibly nonbonding orbital has antibonding overlap between adjacent lobes and so is technically antibonding.  The same is true of the other component of this degenerate pair.  So to make the orbital effectively nonbonding and keep the octahedral structure from blowing apart, we need a large central atom to act as a &quot;spacer&quot; between orbital lobes.  Apparently sulfur is large enough, oxygen is not.