The arguments of ISIL for caliphate and Salafi Jihadists’ critique of it

In the Ramadan 1434, after dominating some areas of Islamic regions, an extremist group related to Salafi Jihadist movement claimed Islamic caliphate and assigned their own leader, Ebrahim ibn Awad Albaqdadi as the caliph of Islamic world. This group, named by adversaries as ISIL, considers the caliphate of Albaqdadi legitimate based on the fact that he has been elected by the "Ahl al-Hall wa'l-Aqd." Furthermore, his dominance and control over some parts of Iraq and Syria is considered as another reason for his rightful caliphate. On the other hand, the other Salafi-takfiri groups, they themselves having a very extreme policy which makes them very close to ISIL, have opposed this bold claim, and strongly have rejected it. These opposing groups address ISIL as Kharijites and the Dogs of the Hell and by rebutting their arguments and putting forward evidences and reasons against this claimed caliphate, try to prove them wrong and warn Muslims not to join them.