Well you could have asked this person to explain instead of just saying “no it’s not.” Also, as far as I’m aware, there’s no reason for positive claims ought to have the burden of proof instead of a negative claim. Any positive claim can be turned into a negative claim by phrasing it in the negative anyway, and positing the non-existence of something still carries the burden of proof.

Anyway, veganism generally has a clear rationale behind it that is widely known, but rarely do I see people seriously arguing that omnivorism is as ethical as veganism. So – burden of proof lies on you I’d say.