Yeah, but the non-rational parts of the brain aren’t good with negation. Reading “animal”, even when suffixed by “-free”, the brain feels it doesn’t want that thing with “animal” on it. Better give it something with “plant” on it.
Why? "Animal-free" means that animals are free, not taking part in the food.
It’s a priming effect. Once your brain sees “animal”, it associates the product or label with animals right away, before higher-level linguistic processing, an association which then has to be undone by the “-free”. That undoing is time-delayed and incomplete.
One common analogy is how when someone says “don’t think of X”, it’s hard to not think of X.
Say, crepes with fruit jam are definitely plant-based, but they may not be animal-free: the jam may contain bits of gelatin, and the easiest way to make nice-looking crepes is to fry them on lard.