The rationale for this is that corporate profits are already taxed. The effective tax rate is about 25% for US corporations. For income from corporate profits to be taxed at the same rate as normal income, it should be taxed at a lesser rate once it's been distributed via dividends or buybacks (which is how the system is set up).
Changing the system would have several negative effects. It would encourage companies to take on leverage. Interest expenses are deductible for the purposes of corporate taxes. While interest earnings are and have always been taxed as ordinary income. So companies would likely shift their balance sheets to compensate. It would also make short term speculative trading more attractive for US citizens (and lord knows we have enough of that). And lead to greater foreign ownership of US equities, which is not necessarily desirable.
There are certainly fairly indefensible aspects of the US tax code. This just isn't one of them.
There's also an interesting argument that it's less distortionary to tax wage income than investment income. Because wages (and especially the variation thereof) are substantially driven by unearned human capital endowments.