I think there's more than one problem raised by running red lights, but one of the problems is that it blurs the line between legal and illegal behavior. Everybody knows that running red lights is illegal, and everybody has seen cyclists do it on a daily basis. Personally, I'm surprised when I see a cyclist observing the law.

Many people, maybe most people, think that perfectly legal behavior, like taking the lane, or even riding on the roadway, is also illegal.

When cyclists do something that is obviously illegal, like running red lights, it makes it easier for motorists to conclude that behavior which seems illegal, like taking the lane, actually is illegal.