That's demonstrably false. Look to cities in northern Europe like Amsterdam and Copenhagen, where bicycle use has caused a massive decrease in automobile traffic.
Add Beijing to the list. However the success of cycling in those cities comes down entirely to geography. Cycling has been popular in those places for a very long time. They also prove that cycling adoption doesn’t come down to infrastructure spending, a city is either geographically suited to it (very flat with minimal sprawl), or it isn’t, no matter how much money you pour down the drain to build cycle ways.
Amsterdam hasn't been big on cycling for a "very long time". It was a very car heavy city for a while and is now on a better track thanks to changes in policy.
As a Dutch person, it was great reading this, because I always assumed that the Netherlands had cycling ingrained in its culture. This would of course make the cycling success of Dutch cities hard to replicate elsewhere. To see that activism and political will played a large role in creating the current cycling climate makes me hopeful it can be replicated elsewhere!