Its an attempt to avoid the long term consequences of population contraction. Most heads of state and policy pushers seek to, at minimum, ensure their country keeps its current level of global influence & power. Generally this holds true whether one is right or left, but some ideological views result in different policies.
A population contraction breaks most existing economic models. You can't borrow money for infrastructure improvements. Tax revenues shrink. Housing prices go down.
The more cynical observer may suspect that its an attempt to break some of the social welfare systems and replace them with more capitalistic alternatives. I'm not sure that is a goal. Perhaps to some it is. In the mid term most certainly you will have to spread about the same amount of resources to a larger number of end users. Two or three generations forward, there should be more resources and economic wealth to make up for this.
An even more cynical observer may believe that the US is trying to destabilize the Middle East because this could have a negative influence on the great powers which threaten global American dominance -- Russia, China, and Europe. There may not be any logistical way for Europe to throttle the influx of refugees. Rather than setting policy Europe is just trying to manage it the best they can. The fall of dictatorships in the Middle East and rise of religious fundamentalism may have been totally inevitable.
The above is all speculation. However, do I believe Western nations accept refugees solely out of kindness and an unwavering moral standing? Probably not.