At least in chess, if it is not the search, then it is probably the evaluation function.

Expert players have likely a very well-tuned evaluation function of how strong a board "feels". Some of it is explainable easily: center domination, diagonal bishop, connected pawn structure, rook supporting pawn from behind, others are more elaborate, come with experience and harder to verbalize.

When expert players play against computers, the limitation of their evaluation function becomes visible. Some board may feel strong, but you are missing some corner case that the minmax search observes and exploits.