Well, paying a lot of tax on your car doesn't mean so much if you earn a lot, so the high car tax has little influence on car ownership or whether people choose to commute by bike or not in Denmark. In fact the longer education a person has, the more likely it is that the person commute on bike.

Most people in Denmark commute on bike because it is fast and convenient. Main reasons for not commuting by bike is distance and time, so these bike highways are meant to make it fast and convenient for people to commute to work, even though they live a little bit longer from their work than the usual bike commuters.

Wide bike paths with two lanes, one for slow, one for fast cyclists, and reducing the number of red light stops by making tunnels and bridges, priority snow removal etc. are all meant to make it fast and convenient all year round to commute to work on bike, even for those that live 10-20 km away from their work in the city.