Post Goa, if LK Advani let status quo (read, Modi in charge) be, he stood to gain nothing. Plus he knew it would be the end of the road for him in the BJP, a party he helped found.
The 'understanding hypothesis' that seeks to explain the psychology of revenge holds that an offender’s suffering is not enough, on its own, to achieve truly satisfactory revenge. Instead, the avenger must be assured that the offender has made a direct connection between the retaliation and the initial behavior.
So he did what anyone would do.
As he went down, he hit where it hurt. It worked. The BJP is hurting.
Post Goa, and the protests in front of his house by Modi-Sena, LK Advani needed to hit back. He also needed the party to know he's hit back. Which explains both the resignation letter, and the 'content' of the letter.
Read more about the complicated psychology of revenge here.