There are a number of factors here which may be relevant, although as observers we cannot be certain which are actually weighing on private decisions.
In favour of the 12th:
- The 12th of December is a Thursday, which is the de facto standard election day in the UK.
- Parliament must be dissolved for a 5-week election campaign. That means that if the election is on the 9th of December, it must be dissolved before next Monday, which is tight.
In favour of the 9th:
- Some people (including Swinson and Corbyn) have raised concerns about students who are registered to vote in their university towns but may already be back at their parents' for Christmas by the 12th. (There is an implied accusation that Johnson wants to delay because the student vote is unlikely to favour the Conservatives).
- Election administrators are raising concerns about the availability of halls to serve as polling stations, because the usual venues may already be booked for Christmas parties, etc. An earlier (and Monday) date would alleviate this slightly.
As to the Lib Dem strategy, they seem to have concluded that there's no realistic possibility of getting a second referendum past the current House of Commons. I saw the suggestion raised at least six months ago (so I'm not sure how easy it would be to track down) that Labour have a red line on a general election before a second referendum because senior figures consider that their manifesto in the last general election would be incompatible with voting for a second referendum, and they don't want to open themselves to the charge of breaking their manifesto.
It has also been suggested, probably with some justice, that being the clear anti-Brexit party is the core policy of the Lib Dems at the moment, so that it's to their advantage to have a general election before Brexit is seen as settled.