how do corporations make their taxable income zero without reducing their true income?

They don't. Well, not for the most part anyway or not in the manner as most folks would think.

I could see a situation where a corp takes accelerated depreciation on an asset or assets for the books but is forced to use a longer straight-line schedule under MACRS. That could conceivably result in a profit according the the GAAP rules once the asset(s) are fully (or nearly fully) depreciated yet result in a much lower taxable income. Most likely that would occur in a weak year following a strong year or years when the assets were being depreciated under GAAP rules. Now that the assets are fully depreciated (or nearly so at a much lower rate than in the early asset life) under GAAP rules there's little or no depreciation expense under GAAP but still some under the IRS rules.

There are unusual situations. Let me provide an example.

ABC Corporation is an insurance company that satisfies all of the criteria under section 831(b) of the IRS code.

ABC Corporation has premium income of $1,200,000. It has operating expenses of $100,000. It has no investment income (i.e., the investment returns were zero.)

Under the IRS codes, the net income of ABC is $1,100,000. However, because it satisfies section 831b of the IRS code, it's income tax is applied exclusively to its investment income (not it's operating income).

Investment income = $0 means income tax = $0, but the income of ABC is $1,100,000

Sometimes they have carry back and/or carry forward losses under Internal Revenue Code 172. This is particularly true on C corp.

The sub S corp, the income of losses flows through te 1040 of each of th "shareholders" (owners).

Who said that they do?