I can't speak for SByer; and in fact I don't agree with him that that
direct oil subsidies are larger than tax income on petroleum. (Although the
indirect subsidies are far larger. The GAO estimates $2/gallon of gas, or an average $12k subsidy per gas car, and they are explicitly
not counting external costs like wars, health effects, carbon mitigation, or military patrols in Hormuz - figures that dwarf all the ones we are discussing here).
However, SByer is correct that there are many oil-specific subsidies, not just the standard deductions that any business can take. VFX posted a long list in these forums (though that was quite a while back).
HERE is a NYT article that discusses some of them.
HERE is an EIA analysis (the EIA was established specifically for protecting Western oil interests, and their last major report argues extremely strongly for ending oil subsidies). And
HERE is even the Heritage Foundation admitting there are oil subsides that should go away - even while they argue that tax treatments aren't subsidies, and for continuing special oil tax treatments.
Part of the confusion is that you and the Heritage Institute are (correctly) noting the technical distinction between things like tax deductions and credits, and a subsidy. However, people that aren't economists (which include most of the people here) regularly use the word "subsidy" to cover all of them - the reason being that the end result is exactly the same. So the common use of the term "subsidy", even though not technically correct, does include the mortgage interest deduction, and the federal tax credit for electric car.
So what many here are trying to say is, oil companies get a lot of special tax treatments and subsidies (in addition to the normal tax treatments), and most people would like to see the special financial incentives go away. Agreed?