There are a few expressions in Japanese where particle で is used but I don't really know which で that one is. それで (translated as and then; after that; due to that) is one of those cases. I basically understand there are two particle で; one used to indicate means of doing something, the use of a tool, and the other で used to indicate a state, condition or form as in である. Probably, most other uses stem from these two categories, so which of these two で is the one used in それで?
それで would be like saying "being that (the reason)"....? If so, in my mind this で is the one used in である.