There are definite cultural problems to blame for this. A significant number of drivers get angry or offended at any non-car vehicle on "their" roads, because they see them as a threat or an impediment them.
There are probably many reasons for this that are not directly related to cars or traffic, but rather to general worldviews, politics, prejudices, aspiration and many others, including seeing bicycles in particular as toys and for recreation by Tour de France-inspired cyclists.
However, I think one of the biggest factors is the insistence on "vehicular cycling"[1], which is the foundation for forcing bicycles to follow traffic laws in place for motorized traffic, instead of having bicycle-specific laws that take into account the properties and limitations of human-powered transport.[2][3]
Forcing cyclists to "take the lane" and perform left turns as if they were cars (and having to cross multiple lanes of traffic) is ridiculous, because of the speed and weight disparity. It's extremely dangerous to the cyclists and aggravating to motorists, because of the huge speed differentials and because a collision will almost always result in severe injuries for the cyclist.
Even the most basic changes, such as making hook turns[4] the mandated method for left-turning cyclists, would make a gigantic improvement in safety and traffic flow. After that comes the bike lanes and paths, plus tweaks to intersections to avoid right turn accidents and reduce the number of times different types of traffic have to cross paths.
The cultural issues of entitlement and refusal to share common infrastructure are a separate issue, but I believe at least some of that tension could be reduced with a few sensible tweaks to traffic laws and road planning.
[1] https://en.wikipedia.org/wiki/Vehicular_cycling
[2] http://shifter.info/vehicular-cycling-is-dead-just-dont-bury...
[3] https://www.youtube.com/watch?v=H75jnRW23X8
[4] https://en.wikipedia.org/wiki/Hook_turn