One person can't make a difference
Demand is the sum of individual decisions and producers respond to it in aggregate. The reasoning also proves far too much: it would rule out voting, recycling and paying tax.
Animal agriculture is a global industry producing billions of animals a year, and one person's purchases vanish inside it: supply chains buy in bulk, stock is ordered in large batches, and surplus is wasted or exported rather than translating into fewer animals raised. Whether or not I buy a particular chicken or carton of milk, the same number of animals will almost certainly be bred and killed, so my individual choice has no real effect on what happens to them. Asking people to reorganise their whole diet for an effect that is, in practice, indistinguishable from zero is asking them to make a real sacrifice for nothing.
Production responds to demand, though not one-for-one: economic analyses of demand elasticity suggest that reduced consumption of a product does reduce the quantity produced, with the size of the effect varying by product and market. The honest version of the claim is that one person's effect is small and probabilistic, not that it is zero.
The structure of the argument is the larger problem. No individual vote decides an election and no individual's emissions change the climate, yet we do not conclude that voting or reducing emissions is pointless. If marginal contribution were the test, almost every collective undertaking would fail it. The growth of the plant-based sector over the past decade is itself the aggregate of individually negligible decisions.
Arguing that an action is not worth taking because it will not, by itself, solve the whole problem. It mistakes a contribution for a complete solution.
How it applies here: Treats a contribution as worthless because it is not individually decisive. Applied consistently this rules out voting, jury service and tax, which few people are willing to accept.
Composition: assuming what is true of the parts must be true of the whole. Division: assuming what is true of the whole must be true of each part.
How it applies here: Reasons from the negligible effect of one person to the negligible effect of the group. The aggregate is precisely what moves production, and it is composed of nothing but those individual decisions.