Shareholders and employees are people. Corporate income taxes represent a form of double-taxation because shareholders are taxed on realized gains (in capital gains or dividends), and employees are taxed on income.

Moreover, capital gains taxes are lower than income taxes because they roughly account for inflation - capital gains are typically incurred on long-term appreciation on assets, and if you're holding something for, say, 10 years at 2% annual inflation you're talking about 21% inflation. So if you have a 21% capital gains rate and a 21% rate of inflation, your effective "tax" rate is really more like 42%.

This is one reason why higher corporate tax rates are generally considered to be a poor economic choice - additionally, corporations can relocate, restructure, and do all number of things to minimize taxable income, and are strongly motivated to do so as rates increase. So you don't even ultimately collect much in additional taxes this way.

Oh, and higher corporate tax rates also raise the price of the goods and services they produce, which is reflected in substantial cost-of-living increases for low and middle-income individuals. That's why it's good politics but bad economics to target corporate taxes in this way.

Because corporations would move.

Individuals don't move as much. So they are in a much worse negotiation position.