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The word 'emergence' is an accent, not an explanation. It shifts focus to the idea that the system itself contains enough power or complexity to produce the effects wanted, when the mistake is to assume that the system doesn't have it. Let's show a simplistic example with ant colonies:

Ant colonies exhibit intelligence.
Ant colonies exhibit intelligent emergent behavior.

In the first statement, there is an easily ambiguated idea that intelligence is part of the ant colonies. This could mean one of many possible things in common speech:
- The ants themselves are intelligent
- The ants are not intelligent, but the colony is well-organized and they act as an intelligent body together.

Both are likely (I'm not an ant specialist) wrong. The problem is that ordinary speech emphasizes the two above interpretations, and deemphasizes the intended one below of "emergence":

- The ants may not be intelligent, and the colony is probably not well-organized. However, the simplistic rules in the ant interactions create a complex system that behaves just like an intelligent body.

That's a lot of space to save by just saying that the colony shows emergent intelligence. A similar accent describes what happens with evolution and emergent traits. The word is intended to shift the focus from the idea that "the two lifeforms developed similar traits as a /direct/ consequence of such and such conditions" to the idea that "under such and such conditions, the two lifeforms happened to develop similar traits".

The system, in this case evolution, more properly describes the mechanism than the situation, in this case the habitat. The word emergent only brings to attention that fact.