Everyone's probably seen Dr. Strangelove at some point in time. If you haven't, stop reading immediately and go watch it. You will not regret this. Those who have watched it are familiar with a contrived, hilarious, but mostly plausible, scheme by which human beings could be fooled into launching an unauthorized nuclear first strike. This is with technology from half a century ago. As you watch this movie, you will be exposed to a system with checks and safeties that can be bypassed by a determined (and insane) individual. Many humans at every step of the process could have stopped the deployment, but choose to blindly follow orders, well, like machines.
What people should be worried about today is how many humans stand between a decision made by a nuclear power's leader and launch. Humans doubt. Humans blink. Humans flinch. When all the data says nuclear missiles are inbound and it's time to retaliate, humans can still say "No.", and have[1]. If you automate humans out of the system, you wind up reducing the running length of a Dr. Strangelove remake. I suspect it would be down to under five minutes today.
Thanks to popular media, we have this strange idea that taking humans out of the equation in automated weapon systems reduces the possibility for error. Individual humans can, and do, make mistakes. This is true. However, humans fix each others' mistakes in any collaborative process. Machines, on the other hand, only amplify the mistakes of the original user. If a bad leader makes a bad decision with a highly automated nuclear arsenal at his or her disposal, how many other humans will have the chance to scrutinize that decision before machines enact it?