What does “haul something out” mean as an idiom?

Solution 1:

To haul something is to [roughly, and/or with considerable effort] drag it up/along. It's not often used metaphorically of memories, along the lines of OP's cited example. The englishforums claim about a "heavy-handed approach to justice" is simply mistaken - the standard idiom, British and American, is "hauled up before the court/magistrate/beak". In respect of memory retrieval, common metaphoric idioms are...

• "to dredge [something] up" - to recall a long-forgotten memory (by implication, not repeatedly).

• "to trot [something] out" - to [regularly] recall and recount the same memory to others.

The title of Dowd's article is a pun on the Sophoclean tragedy Oedipus Rex, and Nichols' father died when he was 11, so we can assume strong associations with the Oedipus Complex (specifically, feelings of jealously and anger towards one's father). Nichols says he often "hauls out" the only two memories he has of his father being proud of him.

The choice of verb emphasises that Nichols finds recalling those memories emotionally taxing. Dredging them up wouldn't work because the memories aren't long-forgotten. Trotting them out might well be valid here, but Nichols probably wouldn't want to use this expression because it's normally said somewhat disparagingly.

Solution 2:

To "haul (something) out" is to retrieve it from storage, generally in order to use it or present it. As cornbread ninja says, if you consider the author's memory as a storage area, it means that he has gone over those memories frequently; or that he has related those two occasions to people often.

The particular passage also carries the subtext that the reason he has to 'haul them out' so often is because those are two of the only times his father was proud of him.