Cars and bicycles are mostly equals in terms of who gets to get first. Though, in cities, it's indeed common for cars to take up a lower, more careful position and they will frequently let bikes go first even if the law may've said they were allowed to go first.

There's just so much stuff going on around you when you're driving a car in an inner city in the Netherlands, that it's wise to drive very carefully. In contrast, bikes have their own lanes, can use both sight and sound more easily and don't have to be so afraid of bumping into pedestrians, this means they have a far better grasp of the situation and possible risks. This combined with higher agility means they can move confidently and adjusted as needed.