I don't speak danish, but according to that graph your claim is not supported
BTW how many people use a bike is a useless metric, how far they travel and for how much time is more important.
Copenhagen is not a good example, it's very small, very flat and public transport is very expensive and it doesn't have to handle the same number of commuters many other cities have to.
For example in Milan everyday a million people come to work from cities around it, in Rome it grows up to a staggering 1.5 millions.
Bike is not favourite because it's better, but because politics made it preferable (less expensive)
Things are changing, Copenhagen had it's first subway only in 2002, decades later other major cities and people will start using it more and more, because the city has invested a lot of money on it and can't handle people not using it or, as it is now, prices have to be very high, which kinda defeat the purpose of a public transport.
Subway it's a good rival for bikes, because they use different paths.
If you increment surface transport in cities with a large number of bikers, they start to compete for road space and it create tensions that need to be resolved.
Bikes in Copenhagen and many other small/medium northern city are the effect of inertia (historically they usesd bikes because it's what they always used), much as the ridiculous number of cars in cities like Rome.
As reference, the Copenhagen subway is run by ATM, the public transport company of Milan (Italy), where prices are an half even though the city is much bigger city, but there are public bikes as well, bike lanes everywhere and lots of car sharing companies.
But the best feature of Milan is still walkability + public transport (subway it's much better than buses and very good on average) because much of the population cannot ride a bike for more than a few kms at a time.
