Q Why don't cyclists use perfectly good cycle paths beside main roads, presumably installed by the authorities at taxpayers expense?
A Well, the answer is that they do, but not all the time, and not every cyclist.
I use one most days, but there are some circumstances where it is impractical. For example, in this country we haven't usually got space to provide a separate path on both sides of a road, so it means that cyclists have to cross two lanes of traffic to access the path. If traffic is light, that isn't usually a problem but if,for example, motor traffic has been held up by traffic lights or a level crossing there will be a whole bunch of frustrated drivers not very keen to have a cyclist of group of cyclists crossing their path just to access the cycle path on the other side. It is easier and safer for the cyclist to carry straight on, and in truth better for the drivers not to be held up too.
Another problem both for the planners and the riders is that because of space the cycle path often is not continuous and peters out after a few hundred yards, and may reappear on the opposite side of the road again. Annoying for everyone.
Often, when there is a T junction with a good cycle path running beside the major road there is no 'drop kerb' to enable cyclists to access it so the road user will have to make a turn into the main road and ride along until there is safe access. It may be that there is an access point just down the road in the wrong direction but even if the rider is local and knows about it, who is likely to go out of their way?
I mentioned 'good ' cycle paths but they are not always good. They don't have to be built to the same standard as the highway, and often they are just wide footpaths re-designated as shared paths.
The lighter surface is easily broken up by tree roots and even weeds can find a crack to grow in and over time cause the surface to decay. A good cycle path can be a joy to ride, and cheerful exchanges with pedestrians and dog walkers as we pass can help to make everyone's day.
Of course an angry cyclist barging its way past innocent pedestrians without warning is never good manners but I have mentioned the dangers of pedestrians with ear buds listening to music or other sound effects and unable to hear a bell or even a shout, and also dogs on long, nearly invisible strings, but these are ordinary circumstances not normally a problem. We all have to share this world with each other.
However, there are some places where cars and goods vehicles get off the road by parking in the cycle path. In those cases it can be impossible to cycle round them particularly if there are several cyclists together.
These are not everyday problems usually, and I believe that cyclists would applaud more usable cycle paths and avoid having to mix with motor traffic, but you did ask why cyclists don't use them.