Kate no longer has Aaron, Jack explains Christian's white sneakers

Jack goes back to his apartment and immediately goes to make himself a drink. Once again, he doesn't even take a single sip before he is interrupted again. He hears a noise and when he goes to investigate, he finds Kate lying on his bed. She has clearly been crying and is now prepared to go back to the island with Jack. When he asks where Aaron is, Kate says "Don't ask questions. If you want me to go with you, you'll never ask me that question again. You will never ask me about Aaron, do you understand Jack?" She kisses Jack and the scene ends, but they presumably had sex.

The next day, Jack makes Kate coffee and pours her orange juice but Kate is acting incredibly distant. Jack moves Christian's shoes which he got from Ray to from the table prompting Kate to question their practicality for the island. Jack tells her that they're Christian's, but when he was in Australia, he told the people preparing Christian's body for transport to just put a ratty pair of white sneakers on him because no one would see his shoes. He also says that "he wasn't worth a nice pair of shoes to me or the time it would take to go out and get them." Kate then asks him "Why hold onto something that makes you so sad?" This from the woman who kept a toy plane for years that reminded her of the mistakes she had made. The phone rings and Kate sees an opportunity to make her exit.

So what happened to Aaron? Did she give him to someone or was he taken from her? What happened in that 24 hours or so that made her do a 180 on going back to the island? Why does she act so strange and distant the next day? One answer we got was why Christian has been wandering around the island and elsewhere wearing his suit with white sneakers. It was an interesting answer that reiterates the sad relationship between Jack and Christian.