The simplest conceivable example of evolving systems is RNA molecules that can replicate themselves. If the replication is similar to modern systems, it always produces a new strand from a single-stranded template. Since all templates will rapidly become double-stranded, the problem of how to separate the two strands has been considered a major issue for the early evolution of self-replicating RNA. The expectation among the experimentalists is that a double-stranded RNA could be copied by strand displacement. This generates two possible templates. Let us suppose only one of the strands, say ($+$), can act as the replicase when single-stranded. On the one hand, copying the ($-$) strand of a double stranded RNA as the template produces a single-stranded ($+$), which can act both as the replicase and template to continue further replication. On the other hand, copying the ($+$) strand produces a single-stranded ($-$), which can only act as the template. A system seems optimal if it always uses the ($-$) strand as the template so as to always produce replicases. Here we investigate whether such preference towards the production of replicases can actually evolve in a system of RNA-like replicators with strand displacement. The results show that if the system is well-mixed, there is actually no selective force acting upon strand preference per se. If, however, diffusion is finite, selective forces `emerge', enabling the evolution of strand preference. Strikingly, however, the direction of the strand preference that evolves turns out to be a complex non-monotonic function of the diffusion intensity. We explain these results by a multi-scale analysis of the replicator dynamics.