Inequality can be a bad thing without being an externality. Externality has a precise economic meaning. Pollution is a negative externality because the byproduct of my voluntary transaction to buy gas and burn it in my car is that you have to breathe the exhaust. You are an external third party that is hurt without compensation. What external third party is being harmed when one person produces a lot and gets rich and another person doesn't?
One economic argument against inequality is that it results in people spending a lot of resources on guard labor. If I live in neighborhood with lots of inequality I have to spend lots of resources keeping the poor people from stealing my things. Therefore, reducing inequality via income distribution can create a public good in the form of less crime (and less resources wasted on protecting property). Thus, you can argue that redistributing income makes sense on the same grounds that having public police makes sense. That is an efficiency argument for reducing inequality.
One economic argument against inequality is that it results in people spending a lot of resources on guard labor. If I live in neighborhood with lots of inequality I have to spend lots of resources keeping the poor people from stealing my things. Therefore, reducing inequality via income distribution can create a public good in the form of less crime (and less resources wasted on protecting property). Thus, you can argue that redistributing income makes sense on the same grounds that having public police makes sense. That is an efficiency argument for reducing inequality.