If he doesn't, then his tax returns would be of great interest to the media and the voters. Unfortunately, you need the tax returns in order to find that out.
The optics of this would be terrible, and would confirm for anyone who was waffling that he is an oligarch.
He already has a reputation for lying, but his net worth goes to the core of his personality. His identity as a "Billionaire", a "Three Comma Club" member, might be a sham.
Possible substantiation of links to the Mafia
He may be spending so much time in Florida so he doesn't have to pay New York taxes.
Possible substantiation of rumors that his charities violate fraud laws
IRS Commissioner John Koskinen said Friday it would be "rare" for an individual taxpayer to be audited as frequently as Trump says he has been.
Most candidates release their tax returns. Barack Obama and Hillary Clinton have both released over a decade of their tax returns. Jeb Bush released his returns from 1981 to 2014. You have to go back to Gerald Ford to find someone who didn't release their tax returns.
But even then, Ford didn't promise to release his returns. On the other hand, Donald Trump said:
2/3rds of Americans- and 2/3rds of Republicans- think candidates should disclose their tax returns. America overwhelmingly believes that a candidate asking for their trust needs to be willing
"There's nothing to learn from them" - FactCheck, (non-partisan)
If Trump Won't Release Tax Returns, His Delegates Should Abstain on First Ballot - National Review, (right-leaning)
"It's none of your business" - Politics USA, (left-leaning)
Editorial: Force Trump to release tax returns - Boulder Daily Camera, (local)
Donald Trump releases personal financial disclosure, but no tax returns - MSNBC, (nominally non-partisan, but observed left editorial)
Here's why delaying his taxes could be disastrous for Trump - Fortune, (nominally non-partisan, but observed right editorial)
Last time Trump's returns went public, he paid $0 - AOL.com, (non-partisan)
What could be in the taxes that Trump has vowed not to release - MarketWatch, (non-partisan, right-leaning editorial)