And that is exactly how you know you have stepped off the rational argument reasoning and into emotional argument reasoning.

Things happen. For example planes fall out of the sky and kill everyone on board. Sometimes they kill people on the ground too.

You can be emotionally afraid of flying (and many are) and of airplanes flying overhead. If you are, then no understanding of the why of a plane crash can re-assure you of its general safety and utility because all you can think about is the aftermath of being in a plane crash.

If enough of the population was emotionally afraid of flying today then we would neither be able to build airports in useful places, nor would we be able to make an economically successful airline. So we would have only very few airlines and airports. Even though the utility of flying and the positive economic impact it makes would still exist, we just wouldn't be taking advantage of those positive features.

For those of us who look at air travel rationally, on a statistical basis it is safer than any other form of travel that allows us to transition from one part of the world to another. We don't spend too much of our time in transit, we get where we are going, and we can get more done in our lives so airplanes are a "good" thing.

For someone trapped in their emotional response, the mere existence of a set of circumstances that would allow an otherwise normally functioning plane to crash, makes airplanes a "bad" thing.

So two things characterize the emotional argument, ignoring probabilities and disbelieving actual examples.

When someone says "<nuclear plant> wasn't supposed to have an issue until <x> happened." and they ignore the probability or likelyhood of <x> happening, you know they are approaching it from an emotional state not a rational state. Fukishima is an excellent example of this type of argument. It takes the form, "Such an event was never supposed to happen, but it did! And look what happened."

Rationally you have to except that anything "can" happen, but some events are less likely than other events. So rationally it was extremely unlikely that a 9.0 magnitude earthquake would strike just off the coast from this plant. That is because 9.0 quakes are themselves exceptionally rare, and earthquakes can happen anywhere along a fault line. So three very improbable things came together, first the fault didn't release any stress until it did all at once (its rare that faults can keep back that much energy), when it did the epicenter was just off the shore of the power plants (it had hundreds of miles up and down the coast which could have relieved the same pressure build up), and the sea mount of the coast dropped literally tones of material into the canyon features of the coast causing a huge water displacement and tsunami (different transitions such as slipping or uplifting cause different amounts of earth movement). If any of those things are different you don't have the issue, multiple quakes instead of one? Not enough energy for a giant tsunami. Too far away? Tsunami's impact is insufficient to wipe out back up power. Fault fails to trigger massive earth movement, no tsunami and no meltdown. So from a rational point of view, this was an extremely low probability event and as such was not explicitly designed for, although as records have shown people have continually suggested adding additional layers of defense to the plant.

From an emotional point of view the argument goes "You said this plant was safe in the event of earthquake or tsunami and yet look, this earthquake and tsunami caused it to melt down!" That argument doesn't care about probabilities it is all black and white, the event "can" happen so you should be prepared for it or you lied.

There are, in fact, a number of things that can cause a nuclear accident that are exceptionally rare. For example, no existing nuclear plant can safely shut down and contain its fuel when it is within the vaporization radius of a nuclear weapon. Nuclear plants cannot withstand the direct impact of meteor with more than 10kg of mass. Nuclear plants cannot withstand the effects of having a magma plume rise up underneath them and breach the surface. From a non-emotion driven point of view, people call these things "impossible" when they recognize that they are actually just very very very unlikely. And they are okay with that. The benefit of the non-polluting, low carbon footprint power is "worth" risking that it would become a mess if it were hit by a meteor.

So an emotional argument puts forth the possible, no matter how improbable, as the evidence for discounting the benefits. This form of emotional argument takes the form, "It's not safe because <x> could happen, and the even if that is rare the cost of an accident is so huge."

And that leads us to the second part of the emotional argument, the perceived cost of failure. The low probability of failure is argued against the huge cost of failure. There actually is a calculus for computing risks and costs, actuaries use it all the time to price out insurance rates, but for nuclear power the potential cost of failure is perceived, by an emotionally framed argument, to be infinite. Both in property and loss of life.

The rational argument is that accidents have a cost and we accept that cost in exchange for a greater good. For air travel we accept that the plane we're getting on might kill us because 99.999% of the time it will deliver us safely to our destination. We know that a catastrophic failure of the airplane at altitude generally means we're dead (and we may find ourselves having many seconds or even minutes to contemplate our impending demise). An emotional argument would frame it as even though an airplane probably won't crash, when it does it kills everyone and so why would you ever take that risk?

But what is the actual cost of failure for nuclear power plants? Nuclear power plants are doubly "safe." That is to say that when they are built they are designed in such a way that only very unusual events or cascades of multiple failures (which from a probability perspective puts them into the rare or unusual category) can cause the plant to fail. That is the first part, the second part is that once they are in "failure" mode, another set of systems are in place to mitigate the cost of that failure. If airplanes were designed this way (and some are) then they are engineered with redundant systems to be highly reliable (safe) and they are equipped with a parachute that can safely lower a non-functioning plane to the ground which deploys in the event of failure (so doubly safe).

The only health threat from nuclear power is exposure to radiation. We know that in a high enough dose, radiation will kill you. It surprises most people but we don't really know what the minimum harmful dose is. That is because we haven't had enough times where people were exposed to ascertain this although Chernobyl has helped in that regard, it provides three interesting cohorts; people who were exposed at the time of the accident and were evacuated, people who continue to live in the area post accident, and people who were not near the event but are otherwise similar (control group). From those groups there is data to support the conclusion that people are a lot more tolerant of radiation than we give them credit for and that in every case when a nuclear accident occurred, when people were notified and evacuated they suffered no ill effects. We also know that people living in Cs137 contaminated environments are affected by the radiation but it is not clear that those effects negatively affect their health, or if they are simply the body's response to living in a higher than normal radiation environment.

As a result, we know that if you live in a country that both has nuclear power and reasonable government that will disclose to you immediately if an accident occurs, then even if you live right next to the power plant and evacuate if you are notified of an accident, then all of our experience tells us that you will not suffer any ill effects. Even if all systems have failed and the reactors are in the process of "melting down" you will have time to leave and be out of the area before anything hurts you. That is a better deal than living in an earthquake prone area like the Bay Area, where, when the Hayward fault shifts (and it will), thousands of people will likely die, unable to evacuate before the event threatened their lives.

So objectively, the cost of a nuclear power accident is not measured in lives (nuclear power accidents have yet to kill anyone who wasn't on the site of the reactor when it failed or trying to clean it up or control it) it is measured in property damage and possibly property availability. Given the probability of things that can cause an accident, it is not as costly as floods along the Mississippi river or Tornadoes in the midwest, or floods wildfires in the west, or oil spills.

But emotionally, its cost is perceived to be much much higher.

Bottom line is that objectively Nuclear Power is solidly a good thing, and as the Times and others like Greenpeace point out could be a big part of attacking the problem of negative human impact on the climate. Climate change being a problem that has the potential to wipe out the entire species. It makes it difficult for someone who understands what is at stake, to understand why anyone would argue against a strategy that could be helping to save the entire planet.

Understanding that argument against, comes from recognizing when it is being made on an emotional basis rather than a rational basis.