I wonder if FDR ever considered turning Italy and Japan against Germany ?
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Duh. Italy WAS turned against Germany. When the Germans deemed that the Italian campaign was not working, because the Italians were losing battle after battle, they intervened. This was so unpopular with the Italians that Mussolini was forced to take refuge, after which he was captured and killed by the partisans.
Japan was too far away for it to fight Germany. The Japanese were simply allies with the Germans and Italians because each was building an empire, and they were agreeing on the turf, so as to not get in one another's way.
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If they did not want Chaos in Iraq they could simply stop supporting the insurgency and start closeing their borders to arms smugglers , since they are facilitateing rather than hindering these things one might presume that they actually wish for all out Bloody Chaos.
Iraq would have a civil war if it were an island in the Sea of Nowhere. Iran and to a far lesser degree, Syria, are a much less important part of this civil war.
God has placed oil under the areas controlled by the Kurds in the North and the Shiites in the South and East. The Sunni areas have far less. The Sunnis are used to running Iraq: they have been ruling since Ottoman Empire times. Shiites are politically like evangelicals and other more emotional religious groups in the US: less education, less status, less money and less respect. The Sunnis do not feel that the Shiites are competent or deserving of running Iraq. They feel the same way about the Kurds, but the Kurds are fellow Sunnis, but a conquered race, and also inferior in the Sunni mind.
Iran considers herself (and is) the defender of the Shiites, and feel that they are living proof that the Shiites can effectively liberate themselves from US domination and corruption better than any Shiite has done. History is, in fact the proof of this. They threw the US out and refuse to allow the US to corrupt their leaders or order them about.
Iran feels that it has a moral obligation to help the Shiites of Iraq to liberate themselves. Iran also doesn't want a huge US army base next door, in much the same way that the US would not wish to see Iranian bases in Alberta or Coahuila.
Syria wants the Golan Heights back above all else, and wants the US out because Israel will be weakened in both Lebanon (which Syrians consider to be an artificially independent part of Syria herself) and Israel. Also, Syria does not want the US to dominate Iraq.
Neither Iran nor Syria want the huge flow of refugees that will pop in on them if the Civil War in Iraq gets worse.
Talking with both Syria and Iran is essential for the US to resolve its problem in Iraq.
Bad intel got us into this mess and a lack of it will certainly not help get us out.