We study the strategic simplicity of stable matching mechanisms where one side has fixed preferences, termed priorities. Specifically, we ask which priorities are such that the strategyproofness of deferred acceptance (DA) can be recognized by agents unable to perform contingency reasoning, that is, when is DA obviously strategyproof [Li17]? We answer this question by completely characterizing those priorities which make DA obviously strategyproof (OSP). This answers an open question of [AG18]. We find that when DA is OSP, priorities are either acyclic [Erg02], or contain an extremely limited cyclic pattern where all priority lists are identical except for exactly two. We conclude that, for stable matching mechanisms, the tension between understandability (in the sense of OSP) and expressiveness of priorities is very high.