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There is only so many copper atoms on the planet, and even fewer in a form that it is economical to extract. It is much better to reuse those than to have to find and dig up new deposits.
Recycling one aluminium drinks can saves enough energy to run a television for 3 hours. This is because it uses far less energy to melt down and recast an aluminium can than it does to extract the aluminium from its ore.
If we don't recycle then the metals tend to end up in land fill sites which themselves are running out of space.