That is an excellent and necessary question and I've been thinking about it. I can tell you that ISIL isn't "just" a terrorist organization. It's announced intentions which it has been pursuing is a Caliphate, a nation that would execute anyone who does not bow to their government. I can tell you that it is not crying out for ignorant martyrs to bomb buildings with no regard to it's goals. No, it's malicious and intelligent. Rather than hoping for aid from sympathetic sources it is working on becoming a regional financial by the forced acquisition of resources. It is self financing and money buys a great deal of power. It ultimately wants religious control, but not for religion sake, but for complete control. ISIL and Saudi Arabia are Sunni, but the former will kill the latter if possible to gain that ultimate power. This goes way beyond anything Al Qaeda wanted, and they were a demonstrable threat. An unopposed ISIL is a disaster in the making, for us, those in the region, and the West in general. The region is of vital importance and it is entirely possible, probable perhap, that they could ultimately shut down ME oil with a resulting economic collapse. There is little evil I can imagine that I believe would be off limits to them if they feel the desire and have the means.
There's all that and I think the argument for the destructive will and potential of ISIL is a good one.
But the real reason I entertain substantial military action happened at 0315 GMT on 19 March 2003. That was the moment where the US declared war on Iraq. That was the beginning of something based on untruths which ultimately unleashed ISIL on the region. We broke Iraq and we bought it. Much ill happens elsewhere, such as in Africa, but what people face in and around Iraq is in great part our fault. So yes I could say it's their problem and leave it at that, but we owe them in ways we cannot repay. Done with careful consideration the removal of ISIL outweighs the accompanying destruction. That's a very cold and calculating statement on my part, but the world is not amenable to arrests and trials. Sanctions, diplomacy, all of that are entirely alien to the mentality of those who go about beheading by the hundreds because they can.
So for me it's mostly about a sense of duty and responsibility to people we supposedly went in to liberate. Lie or not, we went in and are morally obligated to aid where we can.
Just how, when, where, and to what degree that action takes is not something I'm going to guess, but I think we'd better be serious about making things as right as we can.