Hi. I could be wrong but I think your first question to your friend blurred the lines a little. Perhaps it's not "why is your life worth more than the rabbit's" but rather, "why is your will to survive SO strong you'd be willing to take another's life?"
Is this situation (not the beached fish one) any different to "why would you shoot back at someone firing a gun at you and your children/pets/loved ones?" ... Thankfully we don't have guns or such horrendous situations, but just for the exercise ... is it any different? Isn't this the real question? And if it is, then how did meat-eaters get tricked into ignoring that question every time they shopped at the supermarket? "Is your will to survive (in the supermarket chilled foods aisle ... I know, it seems ridiculous) so strong you would buy that chicken breast fillet?" ... or do you have other choices.
As vegans we know eating other animals is ludicrous. Sadly, so. "Will to survive" just doesn't enter into the picture in our Western Lifestyle of Plenty. It is ludicrously irrelevant. And I think it safe to say that most vegans are here because we've seen and felt the consequences.
Back to the scenario: I think ... I might be wrong ... the rabbit would live, not because I'm good at being a vegan, but because by the time I'd worked myself up to deciding I desperately needed to eat it to survive, I'd probably not have the energy to chase it (assuming it's still alive and free). Are they on a desert island or something?
PS: Your friend's next choice, after eating the rabbit, would be "who's next?" (she's with a group of people, after all ... that rabbit ain't going to make a big dish) !!!