In effect you may be owning a very small sliver of the loan the person renting the apartment to you is paying off. By giving them a tax break, their ability to repay the loan improves and as one of the many people who has invested in their success, you get a return on your investment for taking a risk in that market. It's not like that interest saved vanishes. Someone benefits from it. In this case it happens to be the financial system backing the loan as well as the person who took the loan.

Money flows, tax breaks can decrease the viscosity of that flow.

There's more than one way to play the game. :)