I think they should say tax breaks when they mean tax breaks because subsidies sound like direct cash payout to someone. In essence, the tax break for mortgages is a subsidy then. I think when they talk like this they muddy the waters.
Of course, I’m not against getting rid of real subsidies, and I think looking at tax breaks is fine. I just think the language is used pretty loosely and many people are fairly unclear about what they are talking about. Most people don’t consider something like their own tax deductions they might get a subsidy, but using this definition, it is.
It seems to me that since we are the government (although less and less) it is ok to forbid taxing everything. It is up to us to decide what gets taxed. The government is entitled to tax what we let it nothing more. It is not their money.