Mark Wagenbuur has recently uploaded several new videos, one of which shows those situations in the Netherlands where you have cycle paths vs. those where you do not:
Mark explains it all, but I think some clarification and emphasis is still needed for readers from other countries. Minor roads without separate cycle paths have a much lower level of use by motorized vehicles than you might expect. In fact, it is quite normal to not see any motor vehicles until you leave residential areas. These residential streets are in almost all cases not through roads for motor vehicles, so you'll find that the only drivers using them are those accessing properties along the roads. "Rat-running" is a phenomena which is very rare in the Netherlands because in almost all cases there is no advantage to a motorist in using minor roads. Also note that these roads have 30 km/h (18 mph) speed limits. Sometimes the speed limits are lower still, even walking pace. These are roads for locals, and for through use by cyclists.
Once you leave the confines of the residential road and are on roads which do have through traffic by motor vehicle, the design changes. Another of Mark's videos shows a quite typical layout for a road with a 50 km/h ( 30 mph ) speed limit:
And a third video shows an urban dual carriageway, still with a 50 km/h ( 30 mph ) speed limit:
In these cases you see complete segregation of cyclists from motorists. This is what is required to make for a sufficient level of subjective safety that the entire population will cycle. It's what you need if you want parents to allow their children to cycle. Cycling children grow up into cycling adults.
Note the width of the cycle paths. A minimum of 2.5 metres wide for single direction use and a minimum of 3.5 or 4 metres wide for bidirectional use. Also note the separate provision for pedestrians, because sharing space between pedestrians and cyclists never works, that cyclists get priority over road junctions, and that there is a large space between cycle paths and roads. The majority of almost any journey will be in conditions like this.
It can't be emphasized enough that such quality of infrastructure is not optional - it's required for cycling at the level at which it is seen in the Netherlands. The Netherlands is the world's top cycling nation because infrastructure like this is the norm.
These videos were all made in the city of 's-Hertogenbosch. However, they show what is typical across the whole of the country.