Why?
Because he and the PR folks at Mozilla screwed this up so badly.
This reaction was bloody obvious. The PR machine should have been smoothing this transition and been ready for the backlash. They already had a big kerfuffle about his Prop 8 donation years ago.
Not only should Eich be leaving, but anyone in charge of PR at Mozilla should be fired, as well.
No one works those kind of places without having sharpened their Machevelli playbook.
Clearly he failed at that and so should be out on that basis alone, irregardless of appearing to hate the LGBTQ community.
Given that nobody really anticipated Eich being put into the CEO clot, I wonder if some big battle happened in the background. So, the board said "Fine, here's your shot. Enjoy." and dropped him into the soup to let him sink.