The difference between height and those other things the government determines taxes on is that height is not a choice, it's an innate characteristic of a person. People find taxing on height repulsive because it is more or less equivalent to taxing on race which everyone would immediately see as wrong and would be prohibited by the constitution.

In order for this guys argument to hold water he should have used a case other than height which involved a component of personal choice and invoked the same feeling of injustice in people.