What do you think is the maximum output of FUCK of the world's combat forces?
If they all acted at once and with a propose? mostly everyone dies.
You need less than 1% of the world's nuclear bomb arsenal to extinguish humanity.
Read wiki articles on: Nuclear Winter, Nuclear Summer, Firestorm, and Nuclear Capacity by country.
It basically boils down to having 50-100 firestorms in different parts of the world at more or less same time, which creates a nuclear winter which kills many things. Then the gases produced by the nuclear winter itself go even higher and create a nuclear summer. Then if there's anything else living, all the gases essentially destroyed the ozone layer entirely, allowing UVC rays to pass through and mutate the shit out of every single DNA strand on Earth.