It is not an assumption, at least in the standard theory. You start by deriving the valuation results from replication arguments (or, in weaker versions of the theory, some kind of equilibrium model). Then, as a computational device, you observe that you can obtain the same results by taking expectations of payoffs discounted at the pathwise return of some (non dividend paying) numeraire asset under a probability measure where the ratio of any (non dividend paying) asset price to the price of the numeraire asset is a martingale. In a constant interest rate model, the easiest example of this is to pick the risk free asset as numeraire, and we refer to the corresponding martingale measure as risk neutral.
In your example, the forward price is derived by the argument that borrowing money and buying the asset today, costlessly storing it until the maturity date and paying back the loan at maturity will have the same cashflows in all states of the world if and only if the forward price is the one you state.