...is not a paradox at all. Anthony Downs and John Michael Thomson noted that in large cities the average speed of traffic was determined by how long it would take to make the same journey by public transport.
This makes sense; people generally prefer taking their car places, and do so. Traffic gets worse and worse, and the only thing that can make traffic improve is fewer people driving their cars. This will happen at the point that public transport (or biking, or walking) becomes more convenient. Public transport is not easier or more comfortable than taking a car; the switchover point is specifically when taking public transport becomes faster. It is important to note that this calculation works specifically on the door-to-door time, which is to say, the time spent finding parking is taken into account.
It is also important to view this 'paradox' in light of Braess's paradox, the empirical observation that increasing or improving a road network does not reduce traffic congestion, as improvements are balanced by drivers who are incentivized to start driving more. This means that spending on roads will usually make traffic worse, and spending on public transport will make traffic lighter.
The Downs-Thomson relationship has been found to hold true over cities around the world, and is part of the reason that more and more cities are emphasizing public transport and other alternatives to car-based cities.