Arguing about which came first irrelevant now. It's pretty obvious roads these days are designed and built for motorised vehicle use.
If there was a nationwide, good, purposebuilt cycle path system then it wouldn't be an issue. What is issue is vehicles, cyclists, horses and in some cases pedestrians all share same space so conflict occurs at times. Cycle paths as they exist at present are often badly maintained and or in busy areas cars park in them so any cyclists using them are forced to divert either around them into traffic or on pavement area.
Point is that cyclists are perfectly entitled to use the roads. The road infrastructure is perfectly fine while current laws are safe and clear.
Where it goes wrong is when drivers get impatient and ignore the rule of law, or are simply incompetent.