"Carried interest" is when you get compensated for your labor out of the capital gains associated with a project you're working on. It's controversial because it's taxed as capital gains, rather than as "earned income" (which has a higher tax rate). Some people think it's complicated, but the basic principle clearly should be: if you weren't exposed to a potential capital loss, than your proceeds from the deal are not a capital gain.
The special treatment of carried interest is in some sense another example of capitalists giving capitalism a bad name by privatizing profits while socializing losses. In this case, the losses aren't actually socialized, but it's still a case of profits and losses getting differential treatment by the government.
People who consider themselves opponents of capitalism recognize that "capitalists" have too much control of the government, yet their only prescription for this problem is to increase the power of government. The results are sadly predictable.