While older sister Kim Kardashian is busy causing a nude feud on her social media accounts, Khloé Kardashian is opening up on her television show. The topics on Kocktails with Khloé are often silly, ranging from twerk sessions to Twitter wars This week, however, Khloé tackles a more serious topic. Vulnerability. Specifically, what moment of her life has left her feeling the most vulnerable. And it's a pretty emotional one, involving her late father, Robert Kardashian.Khloé said that "one of my dad's wives" tried to tell her that she "was not his daughter" and that "he confided in her. And I was like 'Listen, you can talk about me and my sisters all you fucking want, but do not talk about my dad,' " she says in the clip below. "He's not here."It's unclear who Khloé was talking about, since her father was married twice, and engaged once, after his divorce from her mother, Kris. He also died in 2003 of esophageal cancer. Khloé recently uploaded a picture of she and her father on his birthday, saying she wished they had more photos together.Early in the Kardashian's popularity of their reality show, rumors started circulating that Khloé had a different father than her sisters Kim and Kourtney. Those rumors have likely resurfaced by the attention surrounding the new series American Crime Story: The People vs. O.J. Simpson , featuring her father, a character portrayed by David Schwimmer. Watch below.