How can a train unexpectedly be the wrong way round?

Another common reason why trains don't have the expected composition is a last minute change due to some malfunction of the scheduled train. In such a situation the priority becomes often to have a working train - any train - rather than making sure that the position of the coaches is as expected.

I've even had a case where reservation was mandatory, but the scheduled train was out of order. They replaced with another train, but some people had reservations for seat numbers that didn't exist on the replacement train.

Also the electronic displays on the European continent are not always correct. I've recently had a train in France where the numbering of the coaches the inverse of what was shown on the electronic (so easy to correct, I'd think) signs. It also resulted in people running from one end to the other in both directions. I've never known what was the reason in that case.

This is not really an answer, as David and ptityeti have both covered the reasons why trains may not always have the same "orientation", and why the announcements may not match reality, but illustrates a few more related situations (but is too long for a comment).

• Eurostar trains are (or at least were, not sure about the new e320 train) fully symmetric (they are actually composed of two identical half-sets), with "Premier" coaches in the middle and "Standard" coaches at the ends. So even if they get spun around at any point (AFAIK, the only reason for them doing so would be to have a train do an out-of-service Brussels/Paris trip, or a more exotic Marne La Vallée/Paris Nord), they can just switch the numbering of the coaches (which is of course electronic), and voilà! it's back to normal. The #1 coach is always at the London end.

  Strangely enough, when picking a seat on the Eurostar website, they will tell you that for some seats they can't guarantee which direction they will be facing. Not sure if that was a very, very early anticipation of the e320s being introduced, as the composition of the e300s is really very well determined. Maybe the refurbished (ahem) trains have a different layout?

• in France, TGV trainsets usually have 3 coaches of 1st class, the bar, and 5 coaches of 2nd class (though the exact composition varies a bit, and of course TGV Atlantique trainsets have a total of 10 coaches). In many cases, it would make sense to always have the 1st class coaches at the Paris end (as they are all terminal stations, while most -but nor all- other stations are through stations), but on a given line, you can see both orientations, even for a service at the same time on different days. And with coach-to-platform position indicators on the platforms, you would expect that the train actually matches what is advertised prior to arrival (and it usually is), but I've seen instances of reversed indications which lead to the obvious mad dash (especially as TGVs have compulsory seat reservation).

• some trains, notably the TGV Réseau trainsets have double-numbering of the seats. When you book, you can choose whether you'll be facing the direction of travel or not, and the numbering inside each coach is designed so it can be reversed to match (all seats have two numbers, and only one set is illuminated). That means they reverse assignments within a coach, but the order of the coaches may be different (which is different from what happens on Eurostar trains).

• interestingly enough, other recent trainsets, such as Duplex trains, have electronic seat number displays, so you'd think they could reverse seat number assignments, but they don't provide the "facing direction of travel" option.