It's basically undulations in the normal vagaries of player peformance, that get a chance to manifest to some degree over whatever sample size reality allows.
Saying someone is "not clutch" is a bigger stretch than saying one "is clutch'", which really just means you know -- by way of reality giving them the opportunities -- to verify that yes, they can and will perform in situations that we give some label.
Which again, often times isn't some clutch/non clutch thing, but just facing higher, or different levels of competition. That just goes directly back to player ability and skillset to begin with.
ARod and Papi are perfect examples. Papi gained the reputation as being clutch, but over his career in "clutch situations" he is about the same as he is in "non-clutch situations", people just think of him as clutch, so remember all the times he came up clutch. ARod gets a reputation as not clutch, when in reality if you look at his "clutch numbers" he is about the same as he is in normal situations. People just think of him as not clutch, so they remember all the times he failed in the clutch.