Why do acids ionize in solution if they are covalently bonded?
Because it is energetically favourable ($\Delta{G}&lt;0$) for hydrogen chloride to react with water to form hydronium( $\ce{ H3O+}$) and chloride ions.

Remember that $\ce{ H+}$ does not exist as $\ce{ H+}$ in water, but rather as $\ce{ H3O+}$.