Washington Post speculates that releasing his tax returns would damage Trump's campaign far more than the negative publicity from not releasing them.
With one exception, every U.S. President and every U.S. Presidential candidate has made their tax returns public. Even Gerald Ford, the exception, released summaries of his tax returns covering a decade.
Donald Trump is now the second exception. His first explanation was that he "couldn't" release the his returns due to a pending income tax audit. The audit isn't surprising. In fact, the public information about Trump's business holdings would suggest a perpetual examination of his tax affairs, either directly or indirectly. However, others were quick to explain that the returns could be released regardless of the IRS's examination. Trump later clarified that he was withholding his returns according to his tax lawyer's counsel.
This is a much more reasonable explanation but hardly justifies withholding the returns. This is, after all, a campaign for the Office of the U.S. President, arguably the most important job interview in the world.
Predictably, Hillary Clinton is suggesting that the Trump has "something to hide". It may be that the returns show that his fantastic wealth has been overblown, or that the bottom line taxable income is disproportionately small compared to his public demonstrations of affluence. At the very least, disclosing the returns would almost certainly underscore the economic divide between Trump and his supporters.