You can't build muscle without meat
Muscle growth responds to total protein, training stimulus and calories, not to the source. Plant protein supports hypertrophy when intake is adequate.
Building muscle depends on getting enough high-quality protein, and meat, eggs and dairy deliver it in its most complete and concentrated form, rich in leucine, the amino acid that switches on muscle growth, and easily digested. Plant proteins are lower in leucine and less well absorbed, so anyone relying on them is working against their own biology and will struggle to match the gains of someone eating animal protein. For people serious about strength and size, that gap is real, which is why meat has always been the backbone of athletic diets.
Muscle protein synthesis is driven by the quantity of protein consumed and its leucine content, not by whether it arrived in an animal. Plant proteins are generally a little lower in leucine and somewhat less digestible, which is addressed by eating rather more of them and varying the sources. That is a practical adjustment, not an obstacle.
Controlled trials comparing soya with whey alongside resistance training have generally found comparable gains in strength and lean mass when total protein is matched. Strength and endurance athletes competing on plant-based diets are now numerous enough that the claim is difficult to sustain in the form stated.
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: Sets meat against failure to build muscle as though those were the only outcomes. The variable that actually determines the result is total protein intake, which can be met from several directions.
Defending a generalisation against counterexamples by redefining the category so the counterexamples no longer count.
How it applies here: When vegan athletes are offered as counterexamples, the usual response is to reclassify them (they must be on steroids, not really vegan, or not really serious) rather than to revise the generalisation.