I have no inside knowledge, I assure you, but I have read the Court's rules and a lot of what's been published about the Court. You can get a lot of this kind of info just from reading SCOTUSBlog.
perhaps you'd be kind enough to answer this followup question that your explanation inevitably raises: do Justices make it a practice to discuss these cases privately in sub-groups prior to the conferences, as one would expect, or is there some rule forbidding it that is actually observed?
I have read about intra-chambers discussions before the conference (i.e., most justices will discuss the case with their clerks). I have also read about private discussions between justices after a case is argued, as one bloc or the other tries to pull together a majority. I have never read about pre-conference private discussions, but I am aware of no rule against it, and it wouldn't surprise me if it happened. In fact, that's the only way I can explain the failure to grant cert. in any of the gay marriage cases-- Scalia, Thomas, Alito (and possibly Roberts) all got together and said, "let's vote against cert., we can't trust Kennedy," and Kagan, Sotomayor and Breyer got together and said, "let's vote against cert.-- the country will be more accepting of gay marriage if we put this off for a year or two."
Thank you exceedingly!