Do you agree with Richard Dawkins?

[mediamogul]

That definition escapes speciesism how Mogul? You are assigning "rights" based on metrics determined by species. The vocal supporter of plants rights would say that we suffer in our way, with the equipment available, and that plants suffer in their way, with the equipment available. I'm on your side btw, I don't think that plants have rights, and I don;t think that they suffer the way we suffer...but neither do cattle. So where does that leave us?

Please demonstrate to me that a carrot feels pain and I will eat a piece of bacon this moment.

It's a statement about a plant's ability to feel pain. A plant cannot feel pain or suffer. It's not simply a discrimination about one type of pain over another. Pain is a byproduct of a nervous system and consciousness. Lacking those two things an organism cannot experience pain or suffering. It's not that they are suffering of different types. It is literally that one is capable of suffering and one is not.

A more interesting argument to make might be of an ant. An ant has a basic nervous system capable of pain responses. The ant appears to be suffering when burned with a magnifying glass. The distinction is in that I do not think the nervous system is sufficiently complex to support consciousness. I, of course, have no way of knowing this definitively. I always found this point to be one of the weakest parts of my argument. The problem of consciousness and verifying it in other organisms. I feel comfortable saying that a carrot has no consciousness but can only venture a guess as to whether a fish is or is not conscious.