How is "Consumption tax" considered fair?

Some are in favor of getting rid of the income tax and replacing it with a Consumption tax based (like the name implies) on how much you consume or buy.

The way I see it, this is nothing more than a way to shift he tax burden to the lower and (to a lesser extent) middle classes who spend a larger percentage of their income on things like food, energy, transportation, and consumer goods.

Unless things like stocks, bonds, and other investments that the rich spend more of their money on and the poor can’t afford are also taxed, I fail to see how this can be a good thing, but I also acknowledge that I may be missing something here.

I understand the theory, but I also see too many flaws to make the whole thing seen like a good idea. Would somebody care to enlighten me as to how it could reasonably work?