1) Capital gains are already taxed at the corporate level. People seem to intuitively understand how this works at the dividend level (dividends are paid with post tax dollars), but if you do the math, it works precisely the same with capital gains. (Please note: Tax incidence is complicated. Not all the corporate tax is borne by investors. Especially in small open economies like the UK, it's actually mostly paid by the workers via lower salaries.)
2) Speaking of which...capital gains are a tax on investment. Investment leads directly to increased labour productivity. Productivity leads directly to higher salaries. If we want employees to be paid a lot, we want, as a matter of public policy, to encourage investment. At this point the observant will pipe up "wait, are you saying it's good for the workers if we tax worker salaries more heavily than capital gains income?!" Yes, that's exactly what I'm saying, and it's supported by a rich body of empirical and theoretical backing. Heavy capital gains taxes are the precise policy you'd implement if you wanted to keep labour poor and unproductive. (If it helps, consider that investment is saving - it's an accounting identity - and the US has a big problem with low savings rates, which in turn means that they struggle to get enough investment without borrowing from overseas lenders. See the problem?)
3) Finally, investment income isn't just already taxed at the corporate level - it's also already taxed at the personal level too. Imagine two people, Spendthrift Sally and Frugal Frank. Both work at jobs making $200k/year, after tax. Sally spends all her income on consumption, and saves $0. Frank spends 75% of his income on consumption, and saves $50k/year by purchasing stocks which go up in value by 5% per year. After twenty years, Frank has spent $1m total on stocks now worth a cool $1.7m (clearly he follows the buy-and-hold school of investing). He is retiring, and wants to sell them all to re-invest in safer bonds. What tax rate do you think is fair? He made those investments with after-tax dollars. Do we now tax him again on the result of those investments? Don't we want people to behave like Frank, instead of Sally? And if we charge him 15% on his capital gains, he'd end up paying over $100k MORE total tax than Sally. Does Frank, who has scrimped and saved his whole life, really deserve to pay more taxes than Sally, who never saved a penny?
(The analysis becomes more complicated if Frank received the stock as compensation, instead of purchasing it with his salary. But keep in mind that he's still (1) taxed on that initial compensation and (2) is deferring consumption; a responsible choice which we as a society probably want to encourage.)