DIE HARD question

I was just watching it the other day (almost a yearly tradition) and I'm always confused by the scene between Ellis (Hart Bochner) and McClane (Willis) when Ellis is talking to McClane on the walkie-talkie and telling him to turn himself in and let the authorities handle it. McClane seems to be unusually bothered by this and keeps telling Ellis to shut up and tell Hans that they don't know each other. I always thought McClane was just worried that Ellis would spill the beans that Holly is McClane's wife, but it seems like there's something else at play here but I'm not sure what it is. Any ideas? Of course immediately after this Ellis gets a bullet in the head.
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