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As @WhatRoughBeast's answer alludes to, this a food labelling regulation issue not a linguistic one. In English it's completely correct to call nut milks "milk". Whether a jurisdiction allows you to sell them as "milk" is an entirely different matter.

In the US, it is technically illegal to call plant-based products "milk", "cheese", etc per old FDA regulations. However, the distinction has never been enforced to any degree. Within the last 6 months the FDA has undertaken to understand how people use and perceive terms like milk, in order to determine how to handle the issue. This article is worth reading. While the cases are presumably small in number, soy-based "milk" has apparently resulted in cases of rickets due to Vitamin D deficiency, and rice-based "milk" lacks protein, resulting in Kwashiorkor in infants. Presumably the parents thought they were doing the right thing in avoiding animal products, without realizing that the milk alternatives they were buying did not have the nutritional qualities of the original.

As I understand it, you just need to look at its colour to see why it is called ‘milk’. In the case of almond, the ‘butter’ extracted by grinding the the nut, even when mixed with water, had a milky colour and texture. The liquid from ground soy is so because the beans are not processed till they have a mature ‘beige’ colour and so are again a sort of milky white (unlike soy sauce, where the beans have been dried and the liquid is dark brown.

Coconut ‘water’, as we might drink it straight from the nut, is much clearer. In fact, from my youth I called it ‘coconut milk’. I am grateful to @Chronocidal for correcting my lifelong error. The commercial ‘milk’ comes from the grinding of the white flesh.

Is it technically correct...?

No, of course not. It is neither technically, nor legally correct, for the same reason "fat free milk" (yes, this exists!) isn't, and cannot be.

Technically, milk is an exocrine secretion produced by mammals (in the tell-tale mammary gland) consisting of predominantly emulgated fat in watery solution and casein (protein), some sugars, and some salts. Anything not coming out of an animal's tit therefore is not "milk". Anything not containing a considerable amount of fat is not "milk".

Legally, there are, depending on where you live, more or less hefty regulations such as e.g. the FDA's in the USA, or about half a dozen EU laws in the EU which control pedantically every aspect of what may be called "milk" and "some type of milk" as well as "milk product", including microbiological and technical minimum stadards and minimum fractions in its composition. The word Milk is a protected term, which is basically something like a Trade Mark (similar to Champagne, Camembert, or Nürnberger).

Anything that did actually come out of an animal tit but underwent processing in excess of heating and segregation by skimming is not "milk", and depending on what was done and what composition it now has, it must bear a prefix (such as pasteurized, H-, fat-reduced, etc.).

Milk being sold without animal prefix is (at least in the EU) defined to be "cow milk". Where "cow" should more precisely be "cattle" (but isn't) as "cow" can, depending on the language chosen, be quite ambiguous species-wise. So, e.g. "goat milk" may not be sold as "milk", although it is milk.

Why was it called...?

So why did and do people call white liquids (including the sap that comes out of dandelion) milk? Well for the same reason that diamonds or gems in general (including amber) are stones.

White liquids are white liquids, and milk is a white liquid. 99% of all people aren't biologists or lawyers or overly bright or educated (especially not in the middle ages), and few would care anyway, for that matter. If something looks like a duck, it is called duck.

The scientific or biological definition of milk as a liquid produced by mammals to feed their young does not cover "almond milk".

The food-labelling regulations definition, as it applies to the European Union, is more complicated.

So far, I think I have uncovered four layers:

1. EU regulations say milk must come from an animal;




2. Each country has their own exemptions;




3. Each country has scope to interpret the law;




4. At least two supermarkets have decided to "bend" the regulation, presumably to maintain customer familiarity.

I am not a lawyer, so I ask you to treat this information as such. If you are merely curious about why certain products are labelled as they are, then I hope that my answer is useful. Equally, this issue came about because a German consumer group made a legal challenge against a manufacturer, and I would hope that their counsel was more thorough and more expensive.

1. Following a ruling by the European Court of Justice, "milk" and other milk product names are reserved for animal products.

2. 
   

   However, each member nation has its own exemptions to this rule. Examples for the UK include:

   
   
   
   
   
   • Cream crackers
   
   
   • Coconut milk
   
   
   • Butter beans
   
   
   
   

Exempted Italian products :

• Burro di cacao


• Latte di cocco


• Fagiolini al burro

And everyone's favourite wine :

• Liebfraumilch

3. If this were not complicated enough, there is scope for further flexibility. As a matter of principle, national courts of EU countries are required to ensure EU law is properly applied, but courts in different countries might interpret it differently.
   

4. All four websites for the largest UK supermarkets return results when searched for "almond milk", but only Tesco's and Morrison's advertise it as "almond milk" - Sainsbury's and Asda call it "almond drink".

Looking carefully at the products, none are labelled as milk.