As is usually the case when libertarians and other champions of the most hardline economic orthodoxy make such "educational" pronouncements, the assertion is, all at once, utterly contrary to any conventional understanding of economic reality; Olympian in its arrogance and contempt toward anyone who would presume differently; and opaque in its reasoning.
After all, Investopedia, no bastion of left-wing, communistic thought, defines a subsidy as:
a benefit given to an individual, business or institution, usually by the government. It is usually in the form of a cash payment or a tax reduction. The subsidy is typically given to remove some type of burden, and it is often considered to be in the overall interest of the public, given to promote a social good or an economic policy.Note that "tax reduction" is explicitly included in the definition they provide.
Indeed, one does not find the essentials contested even in the explanation of what a subsidy is provided in the Mises Institute article that seems to usually be at or near the top of the list of search hits on Google when anyone uses it to research the topic, "No, Tax Breaks are Not Subsidies." While the article does charge an "economic and ethical" difference between a cash payment and a tax break (the difference between keeping what you have and being given something taken from someone else), this does not in and of itself make a tax break not a subsidy. In fact, the article acknowledges that "entrepreneurs who take advantage of tax breaks will incur fewer costs than entrepreneurs who don't," and that such breaks are indeed "beneficial to those who claim them"--which is totally in line with the idea that, in conferring advantage to some business at public cost (in this case, forgone tax income, which is shifted to other parties who accordingly bear a greater part of the tax burden, or the burden of forgoing such expenditures), a tax break has the same practical costs and benefits as a subsidy.
So where, one might wonder, is the argument?
The real objection of the piece's author to the term's use in this case appears later, when the article continues with the explanation that government is "not a wealth creator," but only a taker of others' incomes. Because of this such seeming special advantages are really just reprieves from taxation on business that it compares in its various metaphors to a "life jacket in a sea of wealth redistribution," with capitalism only able "to breathe" through such loopholes. Indeed, the web site followed up this piece with another article titled "The Answer to 'Unfair' Tax Breaks is More Tax Breaks."
In short, the "tax breaks are not subsidies" argument assumes that governments have no business taxing business, so that any such taxation is illegitimate (rather than a We-the-people argument for "No taxation without representation" their stance is a pre-1789 French aristocrat's arrogant "No taxes on us, ever!"), and accordingly any respite from such taxation only just, natural, appropriate, and not at all a show of special favor.
None of this is self-evident to most. And when explained to them, most will flatly (and justly) reject the premise of the argument.
Moreover, it will appear the case not only that a subsidy IS a subsidy IS a subsidy, but that, as is so often the case the arrogance and opacity are mere cover for unbelievably shoddy reasoning in the name of the self-serving ideas to which persons and institutions of this type are so prone. Like the claim that one can "never run out of" a given resource, or that involuntary unemployment "cannot exist," an economists' insistence that "tax breaks are not subsidies" is simply a matter of market fundamentalist theologians posing as social scientists, in the way that orthodox economists have been doing for at least a century now; of the staff of right-wing think tanks and the like pretending to be public intellectuals interested in and explaining the actual world rather than PR hacks for the interests that pay their salaries, utilizing theories formed and held without interest in or regard for the real world because they conveniently legitimize their political positions; of the inmates in the asylum insisting that they are really sane while it is everyone else who is crazy.