The correct question is: why do corporations pay taxes? I'll get to that later.
Entrepreneurs start companies in order to make a profit. They make a profit by selling products or services at a price above their cost of production. For instance, they make a widget for $5 and sell that same widget for $10.
Price, while amorphous and confusing, is not arbitrary. It is very easy to determine the minimum price for any product, especially the aforementioned widget. It must be at least $5 because anything less means a loss on every sale. How do you determine the maximum price, that's a little harder. The maximum price is the maximum amount someone is willing to pay for the widget. Any entrepreneur worth his salt is going to charge the most possible to make the largest profit. You may think this means everyone is getting ripped off, not so. Only in extreme circumstances is an entrepreneur able to charge far above his actual cost of production. Competition whittles away at profits to the point where the price cannot go any lower. This is the situation for most prices.
Now my point. We know that the price charged must be at least the cost of production. We also know that there isn't very much slack in the maximum price because competition has eroded excess profits. Finally, we know that the business only exists to generate profits. Drum roll please...Corporate taxes are a cost of production. They are already included in the price and they are always passed on to the consumer.
This brings us full circle to our original question. Why do corporations pay taxes? The answer is that even though the consumer is the one being taxed, they are not aware of it. This is an easy way for government to take more of what you earn and for you not to protest.
Think about it like this. We have two functionally equivalent taxing schemes. The first scheme is to tax the widget after you buy it. The second scheme is to tax the widget before you buy it. Which scheme causes more outrage? The first, because the second scheme hides the tax from the consumer. The effect of the tax is seen in the form of higher prices but the cause it not clear. Most people do not deduce that higher prices are a result of the embedded tax. They attribute it to greed or some other evil motive. While it is true that people may be greedy, I can assure you of one thing: greed by itself is most definitely cheaper than the combination of greed and taxes. The first scheme would make the embedded tax transparent and while the rhetoric of government praises transparency, it's actions are not so clear.