I'm surprised that many people automatically assume "you should cite this paper" means "you should cite my paper". I tell reviewers to cite papers all the time. They're almost never my own papers. They're just relevant papers.

I think there is some aspect here of just finding reasons to dislike the reviewer (though I've certainly had reviewers where those reasons were pretty easy to find).

Agreed, I certainly don't think any request to cite X means the reviewer wrote it. But when there's a vague request to cite more without any indication of what (and sometimes a vague request to cite more on a rather niche topic tangential to the paper being reviewed) I would suspect the reviewer of trying to get their own work mentioned without saying so directly. Because if you know the field well enough to know what literature is missing, then it doesn't take you a moment to paste a couple of citations into your review.