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"We Come Here Because You Go There." That was the slogan of immigrants, legal and otherwise, in Britain in the 1970s. It's even more applicable here and now. The point is that the economic and foreign policies of rich countries often make life unlivable elsewhere, leading to massive population transfers.
If we want to prevent these transfers, we need to change the policies, which should be pretty easy to do, especially because they don't benefit many of us either. Let countries develop like the Asian Tigers or Israel (and others) did, stop forcing Structural Adjustment Programs and "free trade" on them. Alternatively, treat them the way the European Union treated Portugal, Ireland, Greece, and other poorer countries when it brought them in to the Union: they were showered with an infrastructure blitz that dragged them into the First World and prevented massive emigration.
Make Trade Fair! There are no Illegal People!