One (Ellen Siminoff) had planned to leave at the end of 2013, and since she wasn't staying, she didn't want to vote to appoint me only to depart right after voting. That was a clean situation.
I'm bound by non-disclosure not to comment on the other two cases, but this much I'll say based on public info disclosed by others: John Lilly left the board rather than appoint me, as he implied with some tweets at the time. His leaving had nothing to do with Prop 8; he never mentioned it.
Here's what I think happened in the press: Alistair Barr of the WSJ was working on a story about Mozilla being in trouble because Google would not renew its search deal for Firefox, which was due to expire later in 2014 (a highly unlikely claim, but a good link-bait thesis); and also because Mozilla had run for over a year without a new permanent CEO since Gary Kovacs left (true, and a cause for concern among many).
Barr's story was under construction at least as early as February 2014, and it got hot and neared publication later in March as board members resigned. Those of us at high levels at Mozilla believed someone at or near board level who had recently left the company was sending rumors to Barr.
This WSJ story broke on March 28th, and it was summarized at that end of my first week as CEO as "board members resigned a week ago", but then one more week passed, and the Prop 8 story grew bigger due to okcupid, and the "week ago" became bogusly rewritten ("retconned") in many online accounts and comment threads as "three board members resigned over Prop 8".
That never happened. No board members resigned over Prop 8. Mozilla's FAQ on the whole affair says this plainly, and it's accurate on this point.