In the absence of inflation, the social cost of creating a dollar is essentially zero (at most a few cents worth of paper and ink), but the private cost of holding a dollar is a forgone dollar's worth of consumption. Therefore there must be positive externalities to holding dollars.
Inflation increases the private cost without changing the social cost, so magnifies the externality. Moreover, because there's an externality even when inflation is zero, the additional welfare loss due to the first marginal unit of inflation is already non-zero.
This external cost is the same as the shoe-leather costs that FooBar mentions, but thinking about it as an externality lets you measure it as a triangle and so helps toward quantifying it.
