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.
Compare the equivalent product, rice. Rice is stewed grass seeds. You don't think it's a plant product? Are potatoes a plant 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.
Yea. It's still weird as hell to call rice a vegetable as if that's meaningful. Doubly weird to consider rice's vegetable-ness as leading to its carbness.
Most of the rice plant is just fiber, nutritiously.
Fiber is a carbohydrate too, you know. What non-vegetable source of carbohydrates do you know of? As far as I'm aware, human dietary carbohydrates overwhelmingly come from (1) grass; (2) potatoes; (3) fruit; or (4) sugar beets. There is a reason for this: carbohydrate is the basic structural material of plants in the same way that protein is the basic structural material of animals.
I guess you could call honey an animal source of carbohydrates. It's not exactly a huge part of any non-hunter-gatherer's diet. And the bees have to make it from flowers.