Some Questions in Gospel Chronology
A Mediaeval Chronological Table (part of the Alfonsine Tables) from a Mediaeval Manuscript
One reason for the perennial popularity of this activity is its sheer nerdishness! It's fun to get into technical points about the exact start of Emperor Tiberius' reign, or the day of the week on which Passover began in a given year, or the exact relationship between the Feast of Unleaved Bread and the Passover in Second Temple Judaism, even when we can't always be sure of the exact answers. In fact, because of the kind of information and amount of information afforded by the gospels themselves, no definite answers can be offered to many of the questions that arise. So there is always plenty of room for discussion, which is also popular.
Insofar as possible I am trying to deal with questions that involve connecting gospel events with the established chronology of antiquity and not with internal questions of the order of events narrated in the gospels, except when they are tied together. I am not trying to produce a gospel harmony.
It seems to me that the only sensible way to proceed is to take the evangelists' accounts at face value insofar as possible and see how far that takes us in answering chronological questions. In many cases there is no way to know whether, for example, the evangelist in question is recording accurate information, however derived (eg, from tradition, the account of eyewitnesses, or his own knowledge), making an inference on the basis of other information, or (according to some exegetes) constructing a narrative on the basis of ot texts with little regard to actual events. In the absence of certainty, the best way to proceed seems to be to assess each piece of apparent chronological information on its own merits.