Walt...Oswald hated Hosty. He was most angry at the questioner rather than the question.
I don't know if Lee
hated Hosty.... I do believe that Hosty had tried to woo Marina and Marina had told Lee about Hosty's advances. ( If you had met Marina I'm sure you'd understand.... She was a very sexy gal. ( beautiful green eyes)
So lee could have been angry about that, but he was more upset because Hosty had not responded to the note that he had left at the FBI offices. Lee had learned that there was a plot to assassinate JFK on his visit to Dallas and he wanted the FBI to be aware of the plot. Lee was planning on the hoax attempt on JFK, and he wanted the FBI to know that there was a serious plot afoot.
When Hosty showed up at the interrogation, and Lee learned who he was, he became very angry.... Because he had tried to warn Hosty about the plot but the dopey Hosty didn't respond to the note. Lee had written that note hoping that Hosty would come looking for him and then he could tell Hosty what he had learned.