Arnold's a bit hasty to dismiss a compelling line of reasoning:
Suppose that in community Libertopia, in response to customer preferences, all of the better restaurants ban smoking. In nearby community Paternafascista, there is a law that bans smoking in restaurants.
...In both Libertopia and Paterfascista, smokers are not able to smoke in the better restaurants. If someone insists on trying to smoke, he may end up forcibly removed by the police.
...Government policies take away more liberty than equivalent private policies. The reason is not that government policies are backed by physical force. The reason is that government has broader jurisdiction.
Suppose that in Libertopia, you're extremely undesirable, so no woman will marry you. In Paterfascista, you're extremely desirable, but it's illegal to marry you.
In both Libertopia and Paterfascista, you're not able to marry. So you could say that both systems are equally objectionable. But morally speaking, that's highly implausible. In Libertopia, complaints against "the system" amount to "Force someone to marry me." In Paterfascista, complaints against "the system" amount to "Let me marry a willing partner." The first complaint is hard to take seriously; the second complaint is hard not to take seriously.
Bad analogy. Arnold's premise regards equivalent public and private policies. In this case, the proper comparison is not between private policies that prevent undesirable people from marrying and public policies that prevent prevent desirable people form marrying, but between public and private policies that both prevent undesirable people from marrying:
In Libertopia, you are an undesirable potential spouse, and so no one will marry you. So, you move to Paterfascista, only to discover that there, the state deems you unsuitable spouse material, and will not let you get married, even if you could find a willing partner.
Now, if Paterfascista's Bureau of Births, Deaths, and Everything in Between has an infallible oracle for predicting nuptial viability, from one point of view, knowing you are completely unsuitable for marriage saves you a lot of time, money, and emotional energy. You simply know that it's not even worth trying. And since no one is willing to marry you anyway, it's hard to say which of your rights are being infringed upon.
The trouble is that no such oracle exists. Someone who takes Hayek very seriously might say that it is impossible for such an oracle to exist, but even without believing such a theory, we can say that empirically, governmental planning has fallen far short of oracular performance. Therefore, the Paterfascista nuptial policy will inevitably, at the margin, prevent some people who could have found willing partners from getting married.