The fact is, there is no way to prove, or provide evidence for, ANY moral claims - including the claim that killing any animals is bad.
Morality is personal and tribal, always (https://medium.com/the-panopticon-publication/morality-is-personal-and-tribal-always-20c8c31f5d29).
In the absence of a universal moral code, the best we can do is seek what we desire, and try to form collaborative relationships with other people who seek the same things.
Note that this does not preclude empathy and love. We can still desire to save people and animals because we love them or empathize with them. But it is incorrect (and in fact tyrannical) to claim that our love for some animals constitutes a "moral" high ground that others must heed.