Why isn't Almond Milk (and other non-animal based 'milk') considered juice?

Your definition for the word is not sufficiently broad. After all- coconut milk is a thing and it's more like juice than almond and rice milk are.

These liquids are called milk because they are milky: white, opaque, sometimes have protein and fat.

Either way, they aren't much like juice. The nuts aren't just crushed. They are ground and then soaked in water to leach out the good stuff.

I consider "Milk" to be the substance secreted from living being to sustain their young, whether they be human, cow, dog, etc...

Other people consider "milk" to have a wider definition than this. The Oxford English Dictionary (subscription required) gives a number of definitions of "milk" that are relevant to cooking:

1a. A whitish fluid, rich in fat and protein, secreted by the mammary glands of female mammals (including humans) for the nourishment of their young, and taken from cows, sheep, etc., as an article of the human diet.

2a. A milky juice or latex present in the stems or other parts of various plants, which exudes when the plant is cut, and is often acrid, irritant, or toxic. Also: [specifically] the drinkable watery liquid found in the hollow space inside the fruit of the coconut.

5a. A culinary, pharmaceutical, cosmetic, or other preparation resembling milk, esp. in colour. Usually with the principal ingredient or use specified by a preceding or following word. [Here, it specifically mentions soya milk, rice milk, almond milk and a number of alarming medical preparations from former times, such as "milk of mercury".]

5b. milk of almonds = almond milk

7. [originally North American] Strong alcoholic drink, often of a particular type, esp. whisky or beer. Sometimes with a preceding word suggestive of strength or ferocity, as in cougar milk, wild-mare's milk, etc.

For example, Wiktionary gives similar definitions, as will any other dictionary you might care to consult. Your assertion that milk is only the substance mammals use to feed their young is an example of what is known as the etymological fallacy: the belief that, because a word originally meant one particular thing, it must only mean that particular thing today.

It's called "milk" because that is what it most resembles in taste, texture and appearance, and it is also used as a substitute for people who can't or don't want to drink traditional cow's milk.

The choice of what they call it is strictly a product marketing decision, so strict scientific accuracy is not a consideration. What a biologist might refer to as "milk" is not a consideration.

From a cultural viewpoint, the stuff that Taco Bell churns out in no way resembles the actual foodstuffs they are named after. Vegetarian "burgers" are not all that much like the meat "burgers" they take their name from. The green "wasabi" you get at most Asian/Japanese sushi eateries contains no actual wasabi. There is often confusion when talking about what the layperson thinks of as a "theory" vs how science uses the term. Society is filled with examples everywhere of terms that are used that don't strictly fit a technical or scientific definition.

The name is chosen for familiarity and a convenient point of reference for consumers.

I don't think "juice" would not be more accurate, since almonds are seeds/nuts, not fruits or vegetables.

An edible almond is rather dry - and part of it (the shell) is even inedible and not useful to make food of at all. If you just pressed it, without adding water and heat, you would likely end up with impure almond oil and not a thin liquid like almond milk is. This would be like pressing dried beef instead of milking a cow and expecting milk. The same applies to rice, grains, cashews (where using the whole fruit would be actually poisonous!) and most other sources of plant milks.