It’s the word “toutes” at the beginning of the statement which makes the translation “not all women…”

If you wanted to express the idea of “all women don’t like cooking”, you could write

Les femmes n’aiment pas cuisiner.

Which of course is literally “women don’t like cooking”; this is one of those cases where the emphasis isn’t the same as in English, because you lose the “all”. But you can make up for this by writing

Aucune femme n’aime cuisiner.

Which is a clear way to stress that cooking is universally disliked by women.

A structure in which you quantify "all" members of a set and then use a negated verb is also confusing in languages other than French. The problem is where the negation applies.

Would you say this English sentence is any clearer than the French one?

(1) All women don’t like cooking.

Where does the negation apply? Breaking it down, and adding some emphasis for reading aloud:

(1a) [All women don’t] + [like cooking]

== Not all women like cooking.

(1b) [All women] + [don’t like cooking]

== All women dislike cooking.

We fix the confusion by making the negative stick closer to what it applies to: either over to "not all" or else built into the verb with "dislike".

Personally, I find (1a) a little more likely, but another editor by my side leans strongly towards (1b). A similar case is this adage in its classic wording:

(2a) All that glitters is not gold.

It doesn’t mean that what glitters isn’t gold; it means that not everything that glitters is gold. Hence, some people say this instead:

(2b) Not all that glitters is gold.

This usage probably signals a change in how we read the negation, especially considering the original sentence is from the 12th century or earlier and the syntax could certainly have changed since then. (Pedants will tell you that only (2a) is right, but I don’t think you’ll often encounter sentences like (1) or (2a) in casual conversation!)

Now, on to the French… 🙂

Luckily, this syntax doesn’t feel as ambiguous in French (disclosure: this is to my non-native ears). It feels like it must be (1a). That is, the implied "pas toutes" feels like a stronger unit than "n’aiment pas", so mentally it sounds like this:

Pas toutes les femmes aiment cuisiner.

I think pb8330 is on the money by linking this to the presence of "toutes" and gives a great alternative wording for (1b):

(3) Les femmes n’aiment pas cuisiner.

In this kind of structure the "all" is implied. And the "pas" mentally stays where it belongs, with the verb, since this wouldn’t work:

Pas les femmes aiment cuisiner

But it’s true that there are other ways to express the main idea of (1a) that don’t give rise to this confusion.

Ce n’est pas toutes les femmes qui aiment cuisiner.

On ne dirait pas que toutes les femmes aiment cuisiner.

Certaines femmes aiment cuisiner, d’autres non.