From the Huffington Post:
On Friday, the Washington Post ran a meta-piece on the matter under the title: "Is sexual identity our business, or are we a nation of busybodies?" In it, author Karen Tumulty reported that "administration officials asked Kagan directly about her sexual orientation when she was being vetted for her post as solicitor general." It was a slightly interesting revelation, for nothing else than that it demonstrated the topic was on the administration's radar early in 2009.
But a White House official emailed the Huffington Post to push back on Tumulty's claim. It was Kagan who relayed her sexuality, not the White House who asked for it. And the conversation happened recently, not back in 2009.
"Solicitor General Kagan volunteered the information to the White House when media reports surfaced in the pre-nomination process for the Supreme Court," said a White House aide.
Assuming this is true, it shows more of what a careful careerist Kagan is. She had long since resigned to there being lesbian rumors about her and knew that the White House would be too uncomfortable to ask. She also probably suspected Obama wouldn't nominate even qualified LGBT people because... well, that's just who he is.
Can't say I blame her. There's still a lot of homophobia in this world, no matter how much certain blowhards think coming out is a great way for someone to advance their career, it's still an impediment 99% of the time.