What does that have to do with global nuclear war?

It has to do with global nuclear war because saying that one will not break out over 'x' ignores the fact that there's historical evidence for unimaginable carnage being triggered from seemingly minor events. Many scenarios put forward by military thinkers on what might trigger a nuclear war involve escalation – it's not limited to a country deciding to just fire off some rockets.

Isn't the sentiment over WWI that it was only a matter of time and casus belli? If not an assassination then a border skirmish or something else.

I mean, part of the motivation of getting rid of nukes is that 'it's only a matter of time' before someone decides to use them. Nuclear weapons have been around for less than 100 years, so it's not a lot of time to draw conclusions from about how likely Nuclear War is over N years.

Nukes have been used already in war. So I fully agree and would welcome a global disarmament.