We can try to explain this, but forgive me if I make a detour through the general case [if anyone sees something to add or to amend, please come forth].

Meanings of a singular noun

First of all, we should note that a singular substantive (noun) may have four meanings (in French, but also in other langages):

1. A specific object (le chapeau)

2. An object, but unspecific (un chapeau)

3. A quantity of a certain material, or quality [“uncountable“]

4. A quantity of standardized (measurable) material or a standard category of enumerable objects

While the first 2 are clear for most people, the last ones tend to create difficulties.

The magic word “de” (from)

In French, the word “de” is used for these two cases.

Without going into too much grammatical mechanics, we can say that it comes from the Latin preposition de, which meant originally “from” in the sense of location (de urbe = from the city — and btw the verb “derive” <= de-ripare <= de + ripare <= from + to flow, hence “to flow from”). So the word de means the origin, where something is coming from.

But “de” can be also be used, very importantly, for classes of objects or quantities of material (conceptually, you are drawing something from a shelf, or a recipient, etc.).

Note that it can be used for other things, especially to replace the Latin genitive (“Joe’s hat” => le chapeau de Joe, litterally “the hat from Joe”) or to express a connection (la ville de Paris)

Rule for a quantity (3)

a) Use de + defined article

b) de + le is always contracted into du

c) In the negative, the article is dropped

du pain, de la limonade, du courage, ne… pas de pain

[Why rule c) would be interesting; my best guess is that since the original Latin construction had no articles anyway, inserting an article into the already awkward construction of the negative was not very practical; hence French took the least effort path. But perhaps there is another way to explain this.]

Standardized quantity/category (4)

de + noun (no article)

For quantities:

cinq mètres de tissu, trois kilos de sucre, trois décilitres de vin.

The absence of article gives it a formal connotation.

The last sub-case (your question) is the perhaps the most difficult to grasp. Let’s say (though it may seem a little idiotic) that these are cases where there is a quantity of something, but that thing is enumerable. How can one have a singular to describe a number of something that should be a plural?

A few examples should clarify this:

Des études de médecin

Une étude de notaire

Une réponse de Normand (peut-être bien que oui, peut-être bien que non).

In essence, it is the cases where all elements of the category have been fused into a singular noun (approximately: “des études du type pour les médecins”, “une étude comme celle de tous les notaires”, “une réponse typique des Normands”).

And finally your answer, as this is a social category:

Il l’a traitée de vieille fille.

Phew!