I don't understanding the timing either (the flight's too short to get some decent sleep, especially since take off is at 3am), but AUH (as DXB) seem to run a hubbing operation in the middle of the night. I hypothesize that it has something to do with the fact that it can be 50 degrees during the day, which is a nuisance today but would have been a real problem 50 years ago, so night flights became the norm creating a trend, which, once established, is hard to break.

BTW, I note that of the three BA departures from DXB, two are daytime ones, at 1005 and at 1535.

Leaving so late, it's not a fun flight, for sure!