We should ban nuclear weapons because:

• they are the most inhumane weapons;
• today’s nukes are thousands of times more powerful & could kill millions in one go;
• all the other Weapons of Mass Destruction are banned already;
• their risk is unacceptable and accidents happen;
• they don’t differentiate between military targets and hospitals or nurseries;
• they harm and contaminate our environment;
• radioactivity persist for thousands of years;
• a nuclear war would lead to catastrophic global climate change, famine and human extinction;
• we cannot afford 15,000+ nuclear weapons draining our much needed resources;
• they fail to address terrorism and cyber war and  make us a vulnerable target;
• we want to avoid regional nuclear arms races & prevent other countries developing them.

Please have a look here for a more detailed argumentation or visit the resources section.