I don't need to show that eating meat is necessary, Au contraire you need to demonstrate that it's unnecessary.
This is a statement that cannot be refuted because there are an infinite number of ways in which eating meat could be necessary, and you would have to disprove all (infinite number) of them if the burden of proof were on the vegan. For instance, you could just throw out there that "Eating meat is necessary or else the people of Cambodia will starve to death. I won't accept any proof less than a comprehensive and detailed economic analysis definitively demonstrating that this is not the case." And assuming you get this economic analysis in hand? "Eating meat is necessary or else the people of Sri Lanka will starve..." you can just move on to another country. Assuming you get the vegan to give you every single country on earth, then you could pick some other negative consequence. Maybe they won't starve to death but can you prove that us going vegan won't result in them having a political revolution and installing a dictatorship, say? Prove this, definitively, for every country, every subdivision of that country, each city in the world, for every negative consequence, for every point of time in the future. Oh, and this is just a small subset of the full proof, because I'm going to ask you to prove it won't crash some seemingly unrelated industry, for every industry from now until the end of time.
This is already absurd. But wait, it gets worse! Why settle for asking for a possible (but infinitely large) proof when you can ask for an impossible proof? You could assert that "it's necessary in ways you aren't even aware of". This is by definition unfalsifiable because it's a claim that no matter what they can prove, you can assert there is more to prove beyond their knowledge. This isn't just moving the goalposts, this is boxing them up and shipping them out of town. Clearly, this isn't a cogent argument because these are all silly baseless assertions, wherein you're just saying it's necessary to send the vegan on a fool's errand which you can always claim "isn't good enough, prove it for this other area".
Even if you limit it to health, you would need to demonstrate that there's some nutrient that you cannot get in a vegan diet with supplements that you can only get from animals in adequate quantities. This statement can't be disproven, because that would, again, require an infinite search space for all bioactive molecules.
"Sorry I stole your car. It was necessary." ...this almost cries out for the response that asks for proof of the justification. We wouldn't accept "Oh it just was necessary. Trust me. I mean, you can't prove it wasn't."
Similarly, we wouldn't accept this for any other animal. We wouldn't watch someone stab to death a baby dolphin that swam too close to shore and accept "oh it was necessary. Prove that it wasn't!" That argument would be so obviously bad. Why do we suddenly think it's an acceptable argument in this context?