One reason is simple appearance, I think - opaque white liquids or saps have long been called "milky", including nut milks, coconut milk, dandelion or milk thistle saps, and several other white substances. Nut milks get called milk because they look like milk to the eye.
Another reason is that nut milks behave like milks in recipes - they are emulsions with sugars, proteins, and fats... fruit juices tend to have nutrients and sugars, mostly, they behave rather differently in cooking. Almond milk was a long held substitute for animal milk in medieval times because it was more reliable - the nuts would be shelf-stable, while actual milk could spoil within hours. It is worth pointing out that nut milks were substitute for so long because they worked in dishes calling for milk, at both the chemical level and for rough flavor profiling.
Also, it is probably worth noting that nut milks taste like milk, as well - a mellow flavor, very mild and a bit rich. The flavor isn't strong or sweet like other juices. They are different from cow's milk, true, but perhaps nut milks are not immensely more different from cow's milk than it is different from sheep's milk or goat's milk.
In the end, nut milks get called milk because they seem similar, and there's no other category they fit into more neatly. If it is to label them as an alternative, it is a very old label, and for an alternative that works very well in nearly all applications.
Ps: if it helps, the nutrients extracted from the almonds into the milk were produced by the parent tree and intended to sustain the baby almond-plant... so the major difference is that the plant stores the milk in solid form, not whether it was meant for the next generation or not