What psychological stimuli would theoretically drive a person to become an environmental terrorist and perhaps an human-extinctionist?

Being a liberal. They advocate for socialism, equity, etc. All destructive. They perpetuate racist philosophies, etc. They are often times self-loathing too. A lot of the environmentalist ones have actually been responsible for environmental terrorism, destroying infrastructure that resulted in natural disasters, just so that they can "prove a point" about environmentalism. Vegans and vegetarians too, are often times guilty of environmental poisoning issues. After all, how do you feed 7 billion people on kale alone without using pesticides? You dont. Then you have your climate change fanatics and sensationalists. They would rather let the Indian and African populations starve and die in a pre-industrial world incapable of supporting their growing populations by eliminating their access to cheap and plentiful petroleum energy, thereby requiring massive hard, cheap labor and a huge consumption of other resources... than just give them the power they need for infrastructure and development to an innovative 1st world nation that might actually discover a way of getting off petroleum. Oh, and burning petroleum isnt detrimental to the environment in the first place, but never mind that.

Basically its an egocentric and self-righteous and moral-supremacist view of the world, wherein they want centralized power just so long as they are the ones calling the shots. Its very typical of authoritarians. Terrorism is terrorism whether its environmental or not.

Maybe the lost of a loved one

A combination of depression and anti social personality treats/disorders are what drives a lot of the school shooters you hear about on the news.