Letting someone keep their own money is not a subsidy.
It is inherently unfair to provide a homeowner with an interest deduction that is not available to someone who pays other forms of interest on loans (auto loans, student loans, etc.).
If the tax only affects people who don't have the sense to structure their finances to avoid it (by paying the deductable type of interst instead of the non-deductable type), it's like the lottery -- a tax on stupidity. Since you get less of things you tax, a tax on stupidity is a social good.
You'd get to do that anyway even in the absence of the deduction, because your mortgage would cost less in the first place.
It is a subsidy if some people are allowed to keep their money but others are not.
If taxpayers are permitted to deduct the interest on car loans for Ford vehicles but not for GM vehicles, you bet your @ss this is a subsidy.
If the tax only affects people who don't have the sense to structure their finances to avoid it . . .
If I have zero debt and don't own a home, how can I "structure my finances" to take advantage of a mortgage interest tax deduction?