Leila wanted to leave. She would leave if she eventually found her family. Raphael thought it. He knew it with the way she always wanted to find them. What if they were in a different city, country, even? She would always want to spend time with them instead of him.
So instead of saying all this to her, he decided to let her drop the search. He told her he would do it and to back up his claim, he would tell her various things that would make her believe he was indeed looking for them while in real sense he was doing nothing.
A few weeks ago, he had told her he was close to finding them, which got her excited and happy to the extent she stayed over at his place for two days, which she had never done since their relationship began even when he requested.