In most department store catalogs, you'll see all their wristwatches set to this time. The reason is simple and obvious: the hour and minute hands are symmetric across the center of the watch face, nearly 120° from the center axis and from each other. (Remember that the hour hand moves forward a fraction of a tic for every tic the minute hand moves forward; this is why 10:09 is symmetric and 10:10 is not.) In this position, the hands will also neatly frame the brand name, typically displayed on the watch face just above where the hands pivot.
If you were to assume an ideal watch face where the watch tics had infinite precision, you might find the moment of "perfect symmetricity" in the following manner:
50+(x/60) = 60-x
(since the hour hand is positioned at 50+x/60 minutes at x minutes after 10)
x+(x/60) = 10
60x+x = 600
x = 600/61
x = 9.8361 (approximately)
x = 9' 50.16" (to the nearest hundredth of a second)
...but in
real life, the hour hand typically tics forward only when the minute hand sweeps through a full 60 seconds. So instead of
rounding up to ten minutes, you must round down to nine.
The odd thing is that this practice is also carried out with digital watches, even though the above aesthetic reasons are moot. Tradition is a hard thing to buck, it seems.