Why might nuclear energy be controversial?

Nuclear energy can be a very enticing prospect as a replacement for fossil fuels, and it was actually really popular in the 20th century.

Here's some (many) downsides. In order to produce the rods used in nuclear reactors, uranium or plutonium has to be mined, which is as bad as mining coal or fracking for oil. Refinement is also costly process.

Then there's the waste. Nuclear reactors cost millions to build (many times more expensive than building solar panels, windmills or coal-fired power plants), and once they can't be used anymore, it costs millions to take them apart. All of the materials that come into contact with radioactive materials can't be recycled, so they have to be stored somewhere safe. Along with those are the used uranium/plutonium rods, which won't decay for thousands of years. Burying it is costly, and risks contaminating groundwater, escaping containment, or being stolen for malicious purposes.

In the containment shell of a nuclear reactor, water is used to cool the fuel rods. More water is pumped from outside to cool that water (the cooling process happens through a barrier, so the outside water doesn't become radioactive). This hot water is released into an ocean/river/lake, and the heat (thermal pollution) can kill kelp, fish, and other aquatic life. It's better than a coal power plant's emissions, but it's not at all harmless.

Most scientists are in agreement that sustainable energy is not going to come from nuclear energy (especially given the fact that nuclear energy actually isn't sustainable since plutonium and uranium are limited resources). Sources such as biofuels and hydrogen fuel cells, solar, wind, and wave/tidal power are much more viable alternatives to coal, oil, and natural gas.

If you are not a trained scientist, the majority of the information you will learn about nuclear power will come from TV shows, printed publications, or websites. These sources are all created by people, many of whom have political agendas and are not scientists either.

Anything can be made into a crazy, chest-thumping, "oh it's terrible, it's going to kill everyone" propaganda piece, if that's your desire.

The real science is far less dramatic and sensational, but regrettably, the general public will not be interested in it—especially in these days of "4 second attention spans" and "never mind all the details, just give me the basics"

It's debatable because of this; what the actual benefits and drawbacks are is another matter.

Nuclear energy is controversial due to concerns about safety, radioactive waste disposal, potential accidents, nuclear proliferation, and public perception influenced by past incidents like Chernobyl and Fukushima.