Gregory Mankiw thinks taxing inheritance is unfair because it taxes the "Frugals" more than the "Profligates," where these are two high-earning couples, the former of which leaves lots of money to their kids (leading to a tax on the inheritance) whereas the latter spend it all on high living.
I guess I shouldn't be too harsh on Mankiw, as my old friend David Bradford took the same view. But even if one shares the intuition, which I think does have something to it (considered in isolation), it is a woefully incomplete way to look at the problem, making it shocking to me that anyone should seriously think the analysis can reasonably end there.
First, Mankiw is looking at "horizontal equity" (and I'll leave to one side all the issues associated with that framework) solely as to the bequestor generation. Why not also make such comparisons with respect to the next generation that gets the bequests? Again you can have two couples, if you like, but one receives a large inheritance and the other doesn't. So the former is better-off, and if you're into distributive desert (although that's not directly in my own framework) then you could certainly say it has a large morally arbitrary element. Plus, of course, it affects the relative marginal utility of a dollar to the two couples.
Why adopt one framework, exclusive of the other? Bradford, BTW, realized this was a problem, and I think was drawn by the intellectual aesthetics of modeling multi-generational households as unitary long-lived individuals. But he realized that doesn't capture all of the relevant aspects, and was not involved in active political advocacy to anything like the same extent as Mankiw. So he was more entitled to go, for his own private intellectual purposes, with the aesthetics.
Mankiw also, by ending the inquiry there, leaves out all of the empirical issues that might drive one towards (or, to be fair, away from) favoring taxation of inheritances. For example, suppose (as some empirical literature suggests) that people's work and saving decisions respond less to a tax that will only be levied when they die, than to one that is payable while they are still alive, by reason either of their dislike of thinking about their own deaths or of the particular reasons for their leaving bequests (which do not necessarily reduce to valuing children's utility the same as their own - "warm glow" theories, for example, can play out differently).
Or suppose that extreme high-end dynastic inequality has bad effects on a society. Then inheritance taxation may be an important instrument for mitigating these bad effects, although one might also want to consider alternative ways of taxing transmitted capital.