That was the question that Oliver had no idea how to answer. Telling her that he was a vigilante certainly wasn't the way to make an impression and neither was telling her that his family's company was very close to folding. Instead he told her a version of the truth. "I had just taken over my family's company following my mother's death. It was going to be a very long road to get it back on track as she had taken over when my father died. He died in the shipwreck that landed me on an island for five years."
And that was the simple version. There was no Oliver was going to tell her the whole story. That would take a very long time and by the time he done, she'd probably question Oliver's sanity. Sometimes he did.