You are equating your own worth to that of your animals, based on a role they've instinctly assigned to you.
Forgive me, but I'd appreciate if you'd spare me any further explanations and attempts at justifications.
From a purely economical point of view, you may claim that things have only the value you ascribe to them. But I believe in intrinsic, objective worth.
One man's teddy bear is another's broken toy. A person's life, however, is non-negotiable.