The only way to solve problems is to create knowledge. We need to create good explanations of what is there, what it does, and how and why. The only we know to create knowledge is through creatively guessing things and checking our ideas against criticism.
To solve the moral problem of whether breeding and killing animals to eat is wrong we need a good explanation of consciousness, and whether animals are conscious, and if they suffer. We do not have a good explanation of consciousness or suffering yet. Any ideas we do have we can improve upon, endlessly.
Edit: I should emphasize that we can never be certain that we've really 'solved' any given problem: we could always be wrong. This is why we should always be open to criticism and better ideas.