The Islamic State really boils down to a scenario of "Sins of Our Fathers."
The organizations that eventually spawned the Islamic State have long been passed around by both the West and Russia as convenient tools for foreign policy projection. They were funded as if they were simple groups of politically motivated militants who could be influenced and harnessed toward a specific policy objective.
ISIS is a perfect example of the folly of such thinking. What motivates the Islamic State is not a policy agenda from NATO, the Kremlin, DC, or any Illuminati shadow agendas. What motivates the Islamic State is Islam, plain and simple. To the militants who formed the Islamic State, the willingness of the West to sell them the weapons with which to kill their designated enemies is a sort of mana from heaven. They accept it not because they intend to be arms of Western policy - but because it is conducive to their end objective of establishing an Islamic State.
To answer some people who have replied, since: No, ISIS will not contract upon a reduction of western support of regional militants. Part of the reason for this is that it is past a point of no return. The growth of ISIS stemmed from the procurement of surplus turned over to various local authorities upon our departure from Iraq. The damage has been done, and the main resources they are in need of are ammunition, explosives, and fuel/parts - these are well within their ability to supply without any kind of government funding, and many parts of Afghanistan still have stockpiles of Soviet era equipment still packaged in the shrinkwrap. It may not be the best stuff in the world - but from an insurgency standpoint, it doesn't need to be in order to be effective.
The other key thing to keep in mind is that the U.S. offered training to Muslim Brotherhood operatives in Saudi Arabia prior to the war in Afghanistan - specifically in media and propaganda techniques. They trained the militants how to make their warriors and cause appeal to Western onlookers.
Then we have newspaper articles surprised at the number of western muslims who go overseas to join ISIS and cut peoples' heads off.
The thing is that if this were a simple political group - say the Irish Republican Army - our actions would have been completely valid. the IRA has no ambitions to, say, invade and conquer France. Training them to be effective and to throw off British authority would end up with success in the form of an independent Irish state that had closer ties to those who supported its cause (hypothetically).
On the other hand - these militants are motivated by Islam, whereupon the founding charter of the religion makes it clear that the duty of all Muslims is to wage war upon non-believers until the world is entirely subjugated to the religion of Islam.
Training and funding them to overthrow a geopolitical adversary comes back around to bite you in the ass because they have no intention of stopping there - or of excluding you from the list of territories to conquer.