Earlier quoted context omitted.
Bread is made from grass seeds.
So is grain alcohol. That does not make it plant matter. Both are so far removed from "plants" that the association with it's original components is effectively meaningless. Bread is not a plant product, it is its own thing: a bread product.
Grain alcohol, depending on how you prepare it, might easily retain no trace of biological material other than sugar and alcohol. That is not true of bread; bread is not heavily processed at all. You could trivially analyze any sample of bread and determine what plants it was made from.
Claiming that bread is not a plant product makes all the sense of claiming that cheese is not a milk product.