Mortgage interest is also deductible for rentiers. If owner-occupied mortgages were not deductible, it would be redistributing income from those who live in the properties they own, to those who own property and live elsewhere.

Yes, and by the same logic, subsidizing buying Apple shares redistributes profit from people that make iPhones to people that buy them. Why don't we do that instead?

That's isn't actually what subsidizing apple shares would do?

But the answer, is that people who buy and rent out property are generally better off than those renting, so redistributing income between them decreases income inequality.