It's pretty clear to me why mortgage interest is tax deductible--homeowners (and builders, realtors, bankers, etc.) are a very powerful special interest group. This post asks a different question. Why is business interest deductible against taxes on business earnings? Perhaps that also has a simple answer, but that's less clear to me.
Most countries have tax systems that favor debt financing over equity financing. The cost of equity (dividends, etc.) is not tax deductible, while interest is deductible. But why? More specifically, why not eliminate the deductibility of interest, and at the same time lower business tax rates enough so that the change is revenue neutral? That would seem likely to improve economic efficiency, and also lower debt as a share of GDP. It's not obvious to me why this change would be bad.
And it's also not obvious why it would be politically unpopular. Some businesses would gain and some would lose, but in net terms there should be a gain from the greater efficiency associated with lower MTRs on business income. Is the answer that the political muscle of the businesses that would lose is greater than the influence of the larger group that would gain? My impression is that in the US neither political party favors this sort of revenue neutral tax reform. Is that correct? Are there any countries that tax debt and equity equally?
PS. You could make the cost of equity tax deductible, but unless I'm mistaken you would no longer collect any revenue from taxes on capital income.