I encourage you to reread my 2008 article for a sensible take on various controversies.
"In fact, how and when the marriage occurred remains a bit murky, a bill of particulars that I’ve never quite had the courage to explore. There’s no record of a real wedding, a cake, a ring, a giving away of the bride. No families were in attendance; it’s not even clear that people back in Kansas were fully informed. Just a small civil ceremony, a justice of the peace. The whole thing seems so fragile... "
He doesn't spell it out, but as a lawyer and a politician, the whole thing would strike him as trouble: Barack Sr. was already married back in Kenya with a wife and a couple of kids, so getting married in Hawaii would be the crime of bigamy. (This situation was anticipated uncannily in John Updike's 1978 bestseller The Coup, in which an African student in an American college in 1959 keeps trying to tell his white American girlfriend that he has a wife back home in Africa.) Or, you could argue that Barack Sr.'s marriage in Kenya according to the customs of his tribe wasn't a "real" marriage, but that sounds pretty racist. And the whole thing raises the topic of polygamy, which isn't really on-message in American political campaigns.
Obama introduced himself to America at the 2004 Democratic convention with a famous speech that began with 390 words about his ancestry, especially his parent's marriage. It's always been a big selling point for Obama that he unites through his parents' marriage the black and the white, just as Henry VIII united the white and the red roses of the War of the Roses. And, it's been a selling point that his parents' black-white marriage was illegal in many states in 1961 (although not, of course, Hawaii, where a huge fraction of marriages by then were interracial, a subject that Obama supporters don't like to talk about). This is a big part of the self-congratulation that helped get Obama to the White House: look how enlightened we are on race today!
But what's the political utility of the truth about his parents' marriage: that it was illegal because polygamy is illegal in America? The federal government fought a small civil war with the Mormons over polygamy in the 1850s. There's no way, no how to positively spin the fact that Obama's parents marriage was illegally bigamous, so let's not talk about it.
So, what is Obama still hiding?
But, mostly, Obama's big dark secret is that he just didn't do much in his life other than self-promote himself as the guy who should be the first black President. The embarrassing secret is that Obama is President for the same dumb reason as the last guy was President: because of who his daddy was.