The good argument on the side of opposing his CEO-ship was the concern that he would use his position to influence company policy and culture in a way that he couldn't do as CTO. Like most people, I don't know Eich nor have I ever worked at Mozilla, so this initially sounded like a very valid concern.
Eventually, though, it became clear that Eich had done a very good job of keeping his opinion out of the workplace. That's a difficult thing to do, and I don't think I and others were necessarily wrong, at first, to expect that he wouldn't be able to do it. But I read everything I could find on the case, and I never saw anyone even accusing him of intolerant behavior toward gay Mozillians, either in person or in policy -- and he was one of the drafters of the company's diversity policy.
Given that, I think it was unfortunate that the Board accepted his resignation. (It's particularly sad considering that they had talked him into taking the position in the first place.)
Had the Board told him "No, you can't quit; we're going to get you through this" I think they should then have tried to explain that his record on diversity was excellent, and that he and they both knew that the eyes of the world would be upon him, and that people should give him a chance.