Why do you care about animals but not humans?
It assumes concern is a fixed quantity to be divided. There is no good evidence that caring about animals reduces concern for people, and the premise about the individual is usually just asserted.
Time, money and moral attention are limited, and every hour or dollar spent on animals is one not spent on children going hungry or people dying of preventable disease. When someone pours their energy into how chickens are raised while human suffering on that scale continues, it suggests their priorities are badly out of order, or that animals have become a more comfortable cause than people. A movement that asks for moral seriousness ought to show it first toward human beings, and when it doesn't, that gives reason to doubt the judgement behind its claims.
The claim contains a factual assumption and a logical one, and both are weak. Factually, there is little reason to think moral concern is zero-sum: what research exists on empathy points the other way, finding concern for animals and for people positively rather than negatively associated.
Logically, even if some particular vegan were indifferent to human suffering, that would be a fact about them and not about the argument. The soundness of a case does not depend on the breadth of its advocate's other commitments.
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How it applies here: Presents moral concern as a fixed allocation, so that any directed at animals must have been withdrawn from people. Nothing supports treating it as a finite resource.
Dismissing a problem by pointing to a worse one. That something worse exists does not make the thing in question acceptable.
How it applies here: Dismisses the issue by pointing to a more serious one. That human suffering exists and matters more does not make a lesser harm acceptable, or the reasoning about it wrong.