From an excellent post by Richard Kim at The Nation on why "Elena Kagan Is Not Gay:"
I don't know if Elena Kagan sleeps with women or men. I don't know if she sleeps with anyone at all. I don't care. What I do know is that she has never claimed to be a lesbian, that she's never spoken out in the first-person as an advocate of gay rights and that she has never publicly discussed a romantic relationship with a woman. Gay isn't some genetic or soulful essence; it's a name you call yourself–and Kagan has not done that. So in my book, case closed. Elena Kagan is not gay. Is she straight? I don't know, and again, I don't care. Why does she have to have a sexuality at all?
Excellent.