Why are covalently bonded molecular compounds never conductive?

Answer 1

Molecular compounds (these are electrically neutral) would be expected to be poor electrical conductors because the electrons in their covalent bonds are localised and difficult to "move". In any event molecules are separate and possible movement of electrons within the molecule would be difficult to propagate across the intermolecular gap.

There are some interesting examples of covalent compounds that do conduct electricity. There are conductive polymers. Some are carbon based but there are others such as polythiazyl a sulfur nitrogen polymer. Strictly these polymers are molecular its just that the molecules are very large, and they are not usually included in the answers to questions like this. See links

Answer 2

Covalently bonded molecular compounds do not conduct electricity because their electrons are held tightly between the atoms in the molecule, preventing them from moving freely to carry an electric current. In contrast, in ionic compounds, the ions are free to move and carry charge, allowing for conductivity.