The jihadis beheading people on video are following the Nazi playbook from the 30s. Rile up the west enough so they invade and you can then say you're fighting for your homeland. Whereas the foreigners invading are just evil-invaders. They want war because it benefits them (the ones cowering in other countries calling the shots, not so much the ones the smart bombs find and liquify.)
But the US is wrong to engage them how they want. There's always going to be terrorists waging local wars egging the west into a fight. But how will this be any different than operations in the recent past? Will engaging again now prevent future needs to? Of course not. If anything, it'll only make future operations more, not less, likely.
Plot foiled in Australia is more of the same, rile up western countries so they come invade. Westerners on arab soil pisses them all off, not just their militants. It's exactly what they want and why they're doing stuff in western nations.
This is a local matter. Should be fixed, or lost by local soldiers, not international coalitions. If Iraq wants to be Iraq and not IS, they need to fix their own house and not call on the US and others to come every time some militant faction starts blowing things up all over the place. I don't care if every last man, woman, child, and animal falls over dead in the middle east. I'm not a cruel person, but neither am I inclined to fight and die for oil.