The best rebuttals I've heard are
1. Potentially reduces accounting compliance (but the argument is that public companies have this either way)
2. Less frequent taxation (only when owners have capital gains)
3. Creates a greyer area for business expenses, that businesses might fight
4. Regulatory market that REITs currently enjoy (that effectively have this)
The major arguments for it are transparency, simplification, more progressive passive income taxes.
I might be wrong, but I think the system is currently structured such that corporate taxes are mostly a sham anyway; when they pay out dividends, those are taxed at a lower rate to make up for the corporate tax. This is probably anti-progressive because poor people aren't incentivized to invest in businesses, as they'd be effectively taxed closer to rich people rates.
Really, a surprising amount of screwy and circuitous things in our civilization are a direct result of income taxes.