CPA Tax Accountant here - It really is double taxation, as long as you consider the same profit being taxed two different times by the same entity to the same person or people as double taxation. Here is an easy example to follow for the difference between an S and a C Corporation to show how C Corporations have a double taxation issue - there is only one owner of the corporation in the below example (Which is not uncommon for a lot of small businesses).
After all income and expenses, a corporation shows $200,000 of net taxable profit for the year. That $200,000 is then distributed to the sole owner as a distribution/dividend.
If the corporation is an S Corporation, the $200,000 in profit is taxed at the marginal individual tax rate of the owner, as all income and expenses of the S-Corp pass-through to the sole shareholder to their individual return. The $200,000 in dividends are not taxable to the owner (in cases where the owner has positive stock basis at the end of the year). For a single taxpayer, given the above income, they will likely be around the 28% to 33% marginal brackets (depending on other income / itemized deductions, etc) so let us assume 30% effective rate on the profit of the corporation passed through to the individual, for a federal tax bill of $60,000.
If the corporation is a C Corporation, the $200,000 in profit is taxed at the corporate rates - for 2015, $200,000 in taxable income for the C Corporation results in a federal tax bill of approx. $61,250 to the corporation. On top of this, the $200,000 in dividends distributed to the owner is then taxed at the capital gains rate of the owner (let’s assume 15%, but could be as high as 20%), so another $30,000 in federal tax is due from the owner with their individual return for total federal taxes paid of $91,250.
In both of the above cases, the owner of the corporation owns all of the assets of the company and is the sole shareholder, so all profits and dividends are attributable to him alone, yet as a C Corporation, he has to pay additional taxes on the $200,000 profit earned by his company simply because he transferred money from the corporate bank account to his personal account.
I think some of the confusion with this issue is that people usually see corporations as large public faceless entities that pay their own corporate taxes and then the shareholders as individuals who pay separate taxes. But when you reduce down the number of shareholders, people can usually see how the same individual(s) are responsible for taxes for both the corporation and personally.