Actually no... I'm rather on the "yes" side, but that you have the right to something or if you actually get it, or if it's even possible to get what you have a right to, are different things. I mean you too have a right to live, haven't you... but if you fall down the stairs by accident and land horribly, you still won't have a life anymore if you are unlucky.
I prefer to let creatures live if I can, yet I know I sometimes must accept that killing creatures that don't belong in my house can be the only option I have. Of course, I have a cat, and that being said, I can say my cat likes to hunt creatures that don't belong in my house, and I'm not gonna deny that creature to live by her nature when I don't have to.