Crossing the street in Brussels

Today I had an annoying experience. While walking down Boulevard Anspach, near my house, I came up to a pedestrian crossing (of a side street), where the light was red for pedestrians. I looked on both sides, and since there was no car in sight, I started crossing. On the other side there were a pair of policemen, one of whom rudely told me to turn back and wait for the green light before crossing, and I complied (feeling like I was back in Kindergarten).

This got me thinking about what the police force is actually for: fighting crime or teaching people good manners? I mean, the policeman had not justified his command by saying that what I was doing was illegal etc., but that since other people were politely waiting I could too. And anyway, even if it was illegal, is there any reason why it should be a problem for pedestrians to cross even when there is a red light (and no car is approaching)?

Crime rates in European capitals have been rising for years. This is a worrying phenomenon, not least because the level of dicussion is not very high: on the one hand there is scare-mongering by the anti-immigration crowd, on the other Europeans are lulled into a false sense of security by the smug (and apparently incorrect) notion, propagated by subtle anti-Americanism, that crime rates are much higher in the US (see this and this).

Maybe there is something wrong with the approach the police is taking? Isn't it strange that in one of the smaller capitals in Europe, whose "crime rate is in the high range of industrialized countries," that instead of dealing with crime the police should feel it necessary, and have the presumption to teach people to mind their manners?