The Regression Theorem relies on the assumption that the first people to value something as a money must do so based on a memory of its prior use value, with the thing eventually obtaining barter utility and finally monetary value.

No good can be employed for the function of a medium of exchange which at the very beginning of its use for this purpose did not have exchange value on account of other employments.

Ludwig Von Mises: Human Action

Notice that the theory does not merely attempt to explain the origin of the money concept, but of anything that can be a money. In other words, if a good does not follow this progression, it is not money.

The theorem contradicts the subjective theory of value upon which it relies. Value is subjective, which implies it can be based on anything, even if objectively that basis appears irrational.

The theorem fails to terminate its regression by not explaining how a person comes to value something for its original utility. One must assume (not remember) something will be useful if nobody has ever attempted to use it. This assumption of utility is the first valuation, which remains subjective. The first valuation of a thing, like all after, can be for any reason, including its use as a money.

Given a preexisting concept of money, it has been suggested that anticipation of being a money is sufficient to satisfy the theorem. In other words the money does not need to follow the progression in actual practice. In this case, given a preexisting concept of money, anything can begin as money. This interpretation renders the theorem tautological - anything that people value as money can be money. In other words, it reduces to subjective first value.

The theorem is actually based on the empirical observation of monetary evolution. Yet the rational economic theory on which it is based, and the theorem itself, explicitly reject empiricism.

All these statements implied in the regression theorem are enounced apodictically as implied in the apriorism of praxeology. It must happen this way. Nobody can ever succeed in construction a hypothetical case in which things were to occur in a different way.

One of many problems with empirical economics is that new observations can invalidate previous conclusions. Bitcoin has done so to this theorem which purported to be non-empirical. It can clearly be observed that Satoshi intended to create a money, for its first use as money.

The idea is a reasonable empirical theory on the evolution of the concept of money, but invalid as a rational theorem to distinguish money from non-money. Money is distinguished by certain behaviors expressed by people. Concluding that something is a money consists of observing those behaviors, a strictly empirical method.