Their analysis is thus:
1) Utilitarian “optimal tax” suggest that we should tax based on ability (think Marx’s “From each according to his ability”).
2) Income is only partially a measure of ability, as it is related to effort as well, and income taxes discourage effort.
3) Optimal tax theory suggest not taxing things that we should encourage (charitable contributions, mortgage interest payments, educational expenses), thus we should not tax income, as we want to encourage effort.
4) Height is a measure of ability, as taller people tend to earn more, and have a greater opportunity for higher income (they defend this claim empirically).
5) Taxes don’t discourage height, but taxes on height (i.e. “a tall person of a given income should pay more than a short person of the same income”) encourage effort, and results in tall people maximizing their natural ability.
The conclusion: “You must either advocate a tax on height, or you must reject, or at least significantly amend, the conventional Utilitarian approach to optimal taxation.”