Are you asking why electricity doesn’t flow through HCl, or why HCl doesn’t flow through water?
If it’s the former, you’re right, it does have to do with ionization. HCl, as a pure substance, is a solid. It is an ionic compound, which produces a solid crystalline structure often called a salt (not table salt). This solid does not conduct electricity because there are no free floating electrons for the electricity to pass through (unlike solid metals) When you put it in water, the polarity of the water molecules break the ionic bonds of the structure and turn it into positive H cations and negative Cl anions. Because there are ions floating around in this new solution, electricity can pass from ion to ion and have a current.
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