Greg Mankiw often says this:

A tax on height follows inexorably from the standard utilitarian approach to the optimal design of tax policy coupled with a well-established empirical regularity.

Becuase this is part of his argument against income redistribution.  As I have said before (and see a nice comment there by Ilya) this is based on a misunderstanding of the theory of taxation.  It does not matter what the government’s underlying objective is, whether it is utilitarian or anything else.  If the government wants to raise money, for whatever purpose, say to provide education or pay the President’s economic advisors or fight wars, it wants to do so in the least distortionary way.

Minimizing the distortions means making use of instruments that are correlated with ability to pay but are exogenous, i.e. unaffected by tax policy.  As Mankiw points out (the “well-established empirical regularity”), height is correlated with ability to pay and clearly the tax code does not affect how tall you are.  So by conditioning your tax payments (at least partially) on your height, the government can raise the same amount of revenue as a given pure income tax with less distortionary effects on your labor supply.

It has nothing to do with utilitarianism.  (And your natural objection to taxing height therefore says nothing about your attitudes toward income redistribution.)