The answer lies in human psychology. And probably like the old observation about history, people who refuse to understand human psychology are doomed to be victims of psychological manipulation. How is it that even members of peace groups have now come to support US bombing? One lady framed the issue like this: "I request that we discuss and examine why the videotaped beheading of a human being is understood to be more egregious than the explosion (almost totally invisible to the public) of a human being by a missile or bomb fired from a drone."
There are at least four main reasons that explain why Americans care far more about the beheadings (thus far) of two Americans and one U.K citizen, than they care -- here's the polling -- about the thousands of foreign victims of US drone bombing. Here's how people are likely being manipulated into believing that more US bombing is the answer to such terroristic killings even when almost all military experts have admitted that it won't work and "there's no military solution":
1) "Us versus them" mentality, the group bonding also known as tribalism, nationalism, group elitism, etc. seems partially learned behavior but also hard-wired into humans (like other animals) to enable group survival. The worst, most excessive forms of group bonding are also known as racism. Yet it's an innate part of human psychological makeup to identify most closely with those whom we are close to and with whom we share group affinity, so Americans are always going to care more about Americans/Westerners as opposed to more distant foreigners;
2) The gruesome beheadings were deliberately and dramatically videotaped to ensure that US media brought the scenes into all US living rooms whereas the drone bombings of citizens of foreign countries are almost never filmed nor covered at all by US media. Thus to the majority of Americans, drone killings seem sterile, sanitized and surgical even though drone pilots who see the results up close know differently and some are even committing suicide.
3) It's apparent that even a large segment of the "peace" community does not understand that US wars and US-orchestrated regime changes indirectly created Islamic State (and other Al Qaeda type terrorist groups) and that US drone (and other aerial) bombing is giving rise to MORE terrorism, rather than working to reduce it. These two articles "How the West Created the Islamic State" and "How ISIS Is Using Us to Get What It Wants" describe the dynamic. As in all wars, the leaders of both sides are opportunistically using each other to empower each other. Robert Greenwald's video (below) puts it most succinctly: "How Perpetual War Fuels Terrorism." (But the opposite is also true: terrorism fuels war). This is well-known by Western intelligence analysts and foreign policy experts, and it's garden variety war manipulation for everyone except the duped US public. (Borowitz isn't really joking when he reports: "Americans Who Have Not Read a Single Article About Syria Strongly Support Bombing It.") It's depressing otherwise to learn how many uninformed people there are that still think "bombing the village to save it" somehow can work. Such "war on terror" propaganda is actually effective on the liberal-minded who are more vulnerable to having their emotional buttons -- fear, hate, greed, false pride and blind loyalty -- pressed than it is on more pragmatic, cool-headed realists. It's being reported that a number of US journalists who should know better have even fallen for hyped terror threats used to justify the launching of bombing upon Syria.
4) A fourth reason why most Americans now go happily along with perpetual war in a kind of blissful stupor, cheering on their favorite war hawk politician comes from the lessons learned so well from the Vietnam War. Getting rid of the military draft and putting the trillions of dollars of mounting war costs on the ever-expanding and perfectly elastic national debt card was a stroke of genius on the part of the military industrial complex to wipe away any remaining "Vietnam Syndrome." The new "poverty draft" that we're left with constitutes another layer of "us versus them" type manipulation geared to getting the liberal, intellectual middle class on board as they perceive little or no costs and only benefits to perpetual war. Even when not directly profiting by working for military or national security contractors, many Americans have come to believe war creates jobs and ensures they are supplied with cheap gas and other resources.
Anyway, I may be flat wrong but there has to be some explanation and I would welcome others' opinions. Without the witty humor of a Borowitz or Jon Stewart, people may also resent being told how they are constantly duped into this perpetual war that makes them less and less safe. But hopefully, more people will wise up to this psychological manipulation.