He’s messing with words here, deliberately disregarding dishes as a label for a higher-level category of artifacts, as in do/wash the dishes (and in fact in compounds like dishwasher and dishcloth, where the first element dish is understood as a reference to this higher-level category; a dishwasher washes dishes in the broad, not the narrow, sense). Dishes are the central members of this category, but it includes a lot more than dishes.
From a Language Log posting of mine from several years ago on “commercial categories:
“Unlabeled” categories — those that have no relatively brief, conventionalized, everyday, widely used labels that are not just descriptions or enumerations of the things within the categories — are incredibly common, much more common than most people imagine. They are all over the place in domains of meaning that have to do with social groups and relationships and with cultural artefacts of all sorts. But there are contexts in which people want to tap into those unlabeled categories. So they label them [with "semi-technical terms"].
One such context is commerce: in reference to these categories in advertisements, catalogues, directories of goods and services, department designations in stores, and the like. This is what has brought us flatware (or, for some people [note: some people], silverware, regardless of actual silver content, and excluding many items made of silver) for knives, forks, spoons, and serving implements; dinnerware (or, for some people, china, regardless of the constituent material) for plates, bowls, cups, etc. (attempts to describe the referents of such terms tend to trail off into “etc.”); glassware (or drinkware) for glasses of all sorts (glass itself referring usually only to the central members of the category, with wine glasses, martini glasses, champagne flutes, shot glasses, etc. all treated as special cases; glass on its own normally refers to a specific range of types of drinking glasses); tableware for a category that embraces flatware, dinnerware, glassware, and some other items; cookware for, very roughly, pots and pans; bed and bath for yet another category; and housewares for tableware, cookware, kitchen accessories, small appliances, bed and bath, and more, all taken together.
(Cookware takes in pots and pans plus ladles, tongs, whisks, colanders, sieves, graters, and much more.)
The category of things connected with food, cooking, and eating that you wash isn’t covered in this discussion: it embraces (in the terms above) tableware and cookware, but not small appliances, aprons, potholders, hotpads, or a number of other things. We could invent a semi-technical term foodware. But in fact speakers of English — like Jeremy’s mother — just use the ordinary term dishes in a broad sense, leaving it to hearers to use practical reasoning to determine which sense of dishes is the appropriate one. Jeremy is being uncooperative (not for the first time).
(The broad sense of dishes doesn’t get a subentry under dish in the OED, by the way.)