You could obviously make an moral argument, that its the right thing to help the kurds, but thats not even my point. Nobody cares about moral in international relations, so that wouldnt convince anybody.
My point is, that in the long run western countries would benefit from a stable kurdish state/region. The military and politicans are just blinded by shortsightedness. The investment would be resonable low. Western countries (especially the USA) are already delivering massive amounts of weapons to the region. Sadly just to the wrong guys. Western countries also waste big parts of their development aid on dictators or sink it in completely unreasonable projects. Just take this money and support the kurds. Having a peaceful, tolerant and prospering state in this region would have great implications in the (very) long run. The people in the neighbouring countries/regions would see that and would ask their governments for the same. That has the potential to prevent more terrorism and fundamentalism than 10000000000000 drone strikes. It could be a first step to a better understanding between different parts of the world that are fairly hostile to each other.
So why not invest a small amount of money and political capital with little risk on a project with huge potential? Its the reasonable thing to do.