I was asked to explain why nuclear power is inherently and unavoidably unsafe, and will try to give a common sense engineering answer. You know that I am not an expert. This is actually an advantage, because in this case the more people know, the more they say nonsense. Why? Because a little knowledge is a dangerous thing. The nuclear engineering community has answers to all questions they have asked, but the problem is too complex for them to have asked enough questions. Decisions about nuclear power cannot be left to the nuclear power community, the same way that decisions about nuclear weapons cannot be left to the military, and banking regulation cannot be left to bankers. Their excessive familiarity with the subject limits their thinking, distorts their knowledge, and corrupts their judgment.
The amount of energy that can be released by nuclear reactions is enormous. Worse, it can be released very fast, and in a very small space. Even worse, fissile material can continue to release energy for very long period of time.
Nuclear reactors cannot be designed in a safe manner. What can be done is lower the probability of a given undesired event. However, the damage caused by a nuclear disaster is almost unbounded. The total risk will remain very large even if a sophisticated design makes the probability of an individual event small. Contrast that to the worst-case scenario of a airplane crash, or a fire at a thermoelectric plant. Such accidents are comparatively common, however the total damage is limited to people on the plane and at the crash site, or in a neighborhood of the power plant. The area and the number of people threatened by a nuclear plant are incomparably larger. The fact that nuclear accidents are so rare only gives plant operators a misleading sense of security. (Another comparison is to the risk that large, highly-leveraged banks bring to the economy. A failure can cause paralysis to the whole financial system, but bankers reason with basis on the small-scale events that they observe daily. The safer the system, the longer the interval between crashes, the bigger the risk.)
Nuclear reactors cannot be built in a safe manner. The high energy content of the fissile material amplifies the consequences of any disaster. No place is safe enough at the time scales of nuclear fuel decay. Even at the small time scales of reactor operation, disasters happen. Japan is more prepared for earthquakes than anyone else, but still not prepared enough. And earthquakes happen everywhere, not only in Japan. Moreover, nuclear material is an inviting target for acts of war. France, the only one of the 4 major operators of nuclear plants which hasn't had a serious nuclear accident at home yet, built a nuclear power plant in Saddam Hussein's Iraq. Had in not been destroyed by Israel before it could enter operation, it would likely have been the target of Iranian bombs later, with consequences that we can only imagine.
Nuclear reactors cannot be operated in a safe manner. This is a straightforward engineering consideration. In case of malfunction, a nuclear reactor becomes inaccessible and cannot be maintained properly. A disaster becomes inevitable. No design can avoid this consideration, and therefore no design is acceptable from an operational point of view. An appropriate engineering comparison is an iPhone. It is difficult to fix an iPhone if some part goes bad. This is a problematic engineering decision with many detractors. However, it's just an iPhone. If it breaks, it broke. Nuclear reactors cannot be maintained if something goes wrong, and in that is not acceptable.
A common engineering requirement is that a critical system be fail-safe (baka-yoke in Japanese): that in case of failure it goes to a safe mode. The safest fire doors are kept open by electromagnets, and close without any intervention if power is cut. Nuclear power plants are exactly the opposite: they cannot be turned off safely. Even a reactor that has already been turned off is not safe without power.