Why are the only neutral group 6 hexahalides: SF6, SF5Cl, SeF6, TeF6, TeF5Cl, TeF5Br.?

Nessie,

There are hexahalides of the group 6 (or 16) elements that are anions, TeBr₆²⁻ is a random example. So a steric argument isn't particularly convincing. Note that the neutral hexahalides must contain the group 6 element (the chalcogen, Ch) in the highest possible oxidation state for a chalcogen: +6. The high fluorine content of the compounds you have listed suggests that a powerful oxidant like fluorine is required to oxidize chalcogens up to the +6 oxidation state. Or, to put it another way, even if you managed to some how prepare a hexabromide or hexaiodide, it would be unstable with respect to loss of X₂: "ChX₆" → ChX₄ + X₂. Note that other stable +6 oxidation state chalcogen compounds are things like oxo compounds, oxoanions, or their conjugate acids, e.g., SO₃, SO₄²⁻ or H₂SO₄ - made by reaction with another strong oxidant: O₂.

Good luck in your inorganic chemistry course!