In ancient days the caliphate was a religious based state, an Islamic empire intended to encompass all Muslims. Within recent years terrorist group IS (Islamic State) has sought to take over territory in Iraq and Syria to form a new caliphate, but has torn apart social order and lives with their violent methods.  Although the group has mostly been pushed out of Iraq, their activity in Syria is a major contributor to the Syrian crisis.
The emergence of IS groups in Syria has escalated the conflict there to a whole new level. What began as a political insurgence against the Assad regime has become a complicated international proxy war. The Islamic State is arguably the most brutal group in Syria, killing and displacing thousands of civilians and multiplying unrest. The involvement of IS is the reason the United States and other international powers became involved in the conflict. This leads to more weaponry being pumped into the country, airstrikes from abroad, and many more innocent casualties. Because it causes international involvement and increases religious and political tensions in the region greatly, the elimination of IS in Syria is the key to ending the crisis.
Although IS is certainly a factor in the Syrian crisis, it is not the only one or even the primary one. The crisis began because the ruling Assad regime was infringing on Syrian human rights. There are multitudes of religious and political conflicts happening in Syria; the Sunni and Shia religious groups battle, elections are not fair, the Kurdish ethnic group wants independence, and general unrest is widespread. The elimination of IS will help, surely, but it is only one problem in a large set, and won't solve the crisis at its core.
[P1] The main factor expanding the crisis in Syria is the IS efforts to create a caliphate. [P2] Elimination of IS will solve the crisis.
Rejecting the premises
[Rejecting P1] IS is not the main factor, the Assad regime is. [Rejecting P2] Eliminating the problem of IS will not solve the other issues in Syria.