They had one. Until he made a fatal mistake of giving a tenner to the wrong people.
But then he went on to make Yet Another Chromium Fork, so it doesn't seem like he was particularly attached to Gecko or what it stands for in the browser engine market anyway. What's to say that Mozilla wouldn't have given up the fight and pivoted to Chromium, like Opera and Edge did, if he was still in charge?
Eich chose to resign due to internal and external protest in the form of petitions and resignations.
No one forced him to do anything, and Mozilla itself certainly didn't force him out.
His free speech was met with the free speech of others, and he decided it was too painful to stay in that spotlight.
How would you prefer it to have gone?
Translation: he had donated to ban same-sex marriage in California[1]
[1] https://en.wikipedia.org/wiki/Brendan_Eich#Appointment_to_CE...
He gave $1000 donation to support a ban on gay marriage, to be clear.