You'll be deficient in B12
This one is half right: a vegan diet does require a reliable B12 source. It comes from bacteria rather than from animals, and a supplement or fortified foods settles it.
Vitamin B12 is essential for nerve function and blood formation, and no plant food reliably supplies it, so a diet with no animal products cannot meet this basic need on its own. A way of eating that only works with a daily pill or industrially fortified products is not one humans are naturally suited to, and deficiency can develop silently over years and cause nerve damage that may not fully reverse. Meat, eggs and dairy deliver B12 as ordinary food, which is strong evidence that animal products belong in the human diet.
B12 is produced by bacteria, not by animals or plants. Grazing animals acquire it from soil and from their own gut flora, and farmed animals are routinely given it as a supplement: a good deal of the B12 in the food supply has already passed through a tablet on its way to the plate.
For anyone eating no animal products, a supplement or fortified foods is necessary rather than optional, and this is the point on which the objection genuinely lands. It is an argument for planning a vegan diet properly, not an argument against one. Deficiency is also common among older adults and anyone with impaired absorption, irrespective of diet, so periodic testing is sensible for most people.
Presenting two options as though they were the only ones available when further options exist. Also called a false dichotomy, or black-and-white thinking.
How it applies here: Frames the choice as eating animals or being deficient, when supplementation is a third option: and one the livestock industry already depends on to keep its own animals replete.