There are many good reasons to oppose the use of nuclear energy. Nuclear power installations are vulnerable for accidents, incidents and attacks. Radioactive material can be disseminated. Radiation is harmfull and can, even in small quantities, be lethal. Contamination with radioactive material can make entire regions uninhabitable for thousands of years.
Even during 'normal operation' nuclear power stations (and other installations) disseminate radioactive materials. The nuclear fuel chain is complicated and in every step transport is needed. These transports are in itself vulnerable for accidents, incidents and theft. Radioactive material in the 'wrong hands' leads to a horror-scenario. The use of nuclear power leads to the production of large quantities of dangerous radioactive waste. Although the nuclear industry has been seeking for solutions for more than 6 decades now there is still no country in the world that has found a scientific sound way to deal with its radioactive waste.
It does not take much to build a nuclear weapon ones you have access to the material, knowledge and infrastructure provided by the 'civil nuclear fuel chain'.
Nuclear power plants are extremely expensive and hard to finance. Only when supported by public money a nuclear power station is build. In almost all countries risks and non-direct costs are passed on to the government (the public, the taxpayers); longterm management of the waste, security of the nuclear power plant, costs of transport for instance. It is impossible to insure your nuclear facility on the private market. So in all cases it is the government again who guarantees the compensation for accident-related costs - which is in itself again impossible. The Fukushima disaster in Japan is estimated to costs at least $143 billion. The nuclear disaster in Japan has tragically demonstrated how unsafe nuclear power can be. The chance that a major accident happens is maybe slim but the consequences are devastating.
A nuclear power station itself does not emit greenhouse gasses like CO2. Yet nuclear power contributes to climate change; with every step in the whole fuel chain, needed to in the end generate electricity, many energy is used. For instance, the extraction of uranium and the enrichment of uranium are extreme energy-intensive processes. Life-cycle analysis of the whole fuel chain clearly shows the contribution of nuclear power to climate change.