What motivation does the show present for Andrew Cunanan assassinating Gianni Versace?

American Crime Story recreates real life crime stories. But the problem with the 2nd season was that Andrew Cunanan was never caught and tried for the murder(s). So there is no official record of Andrew's motivations in killing these 5 people. The showrunners have created a fictitious character of Andrew Cunanan which may or may not be faithful to the real life version. After all, they only had vaugue bullet points and hearsay to go on.

As depicted in the show, Andrew's motivations for killing the other four people are relatively clear.

1. Jeffrey Trail - jealousy, betrayal. He suspected that Jeff and David were having an affair behind his back.
2. David Madson - rejection. Andrew proposed to David multiple times but he rejected. David was the love of his life and Andrew could not bear the rejection. Also, David was witness to Andrew murdering Jeff.
3. Lee Miglin - jealousy. Lee was reputed and wealthy, which was Andrew's dream. So he wanted to ruin his reputation by outing him as gay. Hence he staged the murder scene with gay pornography.
4. William Reese - unlucky witness. Wrong place at the wrong time, when Andrew stole his truck.
5. Gianni Versace - ???

Andrew met Gianni two times as I recall. First in a pub and second in an opera where Gianni invited him. In the final scene of the series, we see that Gianni rejected Andrew's offer of being his assistant.

So, why did Andrew murder Gianni Versace in this story? His motivations were clearly presented for the other four murders, except the last one. And since the show is titled Assassination of Gianni Versace, I expected it to be so. I am not asking for why the real Andrew killed Versace, but what motivation the show attributes to him, as it did for the other murders.

Is there dialogue or scenes in the 9 episodes that I may have missed that concretely present or at least imply his motivations for killing Versace? If not, then did the showrunners, especially Tom Rob Smith, comment on their interpretation of his motivations in the show? After all, they created this fictitious character of Andrew Cunanan, which may or may not be consistent to his real-life self.