Nope. It is quite possible. There are several possible extinction level events that have been theorized.
Possible ELE's:
impossible impossible
Killing everyone I see.
oh! its a very hard question dear :* It is impossible to get everyone to like you!
When he killed Polonius he thought he was killing Claudius. Everyone else he killed, he killed on purpose.
Almost everyone
they accomlished it by killing everyone and won!
She flooded the whole facility with "A deadly neurotoxin" killing everyone in the facility.
Frogs eat flies so instead of killing the fly ,which is impossible the frog eats the fly whole
by killing everyone
It's killing everyone every where
The question presumes the impossible. There is no Illuminati, and what does not exist cannot kill anyone.
purges and by killing everyone who looked at him funny. ;)