(1) If I buy a property and rent it out, then my income is equal to the rent that I get, minus expenses, including interest payments on a mortgage. Thus, I get to deduct mortgage interest.
(2) If homeowners could not deduct mortgage interest, then landlords would have an advantage. That is, the landlord could deduct mortgage interest, but the homeowner could not.
(3) As a homeowner, I do not count as income the “rent” that I earn on the house. This gives me an advantage over a landlord.
(4) Also, I do not count as income a capital gain from selling the house. This is another advantage over a landlord.
One can argue that the main distortions in the tax code are (3) and (4), rather than the mortgage interest deduction. If you took away (3) and (4), then I think one could argue that you want to keep the mortgage interest deduction.
Of course, the main reason we have the mortgage interest deduction is that the mortgage industry loves it. Yes, it is popular with people who currently use the deduction. But even if you “grandfathered” the deduction for everyone currently using it, you could never get a repeal past the housing lobby.