Kane Baker has a YouTube video in which he introduces the word 'wulture'. 'Wulture' applies to all things that are vultures, and excludes all things which are white. Delia is a white vulture. He asks: What is so objectionable about considering Delia both a wulture and a non-wulture?

This got me thinking: How does one really justify the law of non-contradiction without just appealing to intuition? It could be said that the idea that to reject it would be self-defeating because then you open yourself up to the idea that the law of non-contradiction could also be true. But this issue doesn't really apply when we have limits on what contradictory statements are true. Delia being a wulture and non-wulture doesn't necessitate that 'the law of non-contradiction is true' and 'the law of non-contradiction is false' are both true.

So, can somebody please give me a justification of the law of non-contradiction which doesn't just rely on intuition? Is it possible? I think I have reason to believe that metaphysically speaking there is not contradiction, so I am specifically talking about propositions, even if they're just semantic.