'Mopeds'. These have hardly been seen in this country since the 70s. What I think you mean are step-through scooters, which are significantly more powerful than mopeds ... and can be ridden legally on a 'Learner' license without ever passing a proper riding test. These are often ridden by frustrated car drivers on their car license (which is why the L plate). Such people often have no training on two wheels at all, which is why you see them overtaking illegally on the zig zag lines at crossings all the time.
'Cyclists'. Ok you've had a shitty experience involving someone on a bike - probably more than one experience I'm assuming, so therefore all cyclists in your view a 'f**king idot w****rs' are they? Nice one. There plenty of people who ride bikes who are sensible and respect the road, but unfortunately those such as you have described are the ones who stand out. I've had plenty of shitty experiences on my bike vs motorised vehicles - such as the black cabbie who turned left across me recently with no left indicator having overtaken me from behind ... and then yelled at me for getting in his way. I don't think bad of all car drivers just because of this dick. In fact, I am a car driver myself quite often as are a lot of cyclists - very few people stick to a single mode of transport.
'Training'. The many cycle campaign groups such as the LCC do in fact run regular training sessions for new cyclists. You can see them at strategic cycle commuting spots all over London, offering their bike check and training services to commuters.
'Red Lights'. Jumping red lights in the 90s used to be the preserve of a dispatch rider. Depressingly the increasing numbers of converted car drivers are copying them, thinking its the done thing and abusing their new found freedom. Those of us who have been on the roads any length of time know why this is stupid and wait patiently at the lights along with the cars ... I tell you though, the ASB (advance stopping box) designed to keep cyclists safe is a scary place to be when the lights go green and the horde of motorbikes, cars and other larger vehicles are stuck behind you wanting to get going!
'Insurance'. Actually more people than you probably think do have insurance. People such as your BMX idiot would never have it even if it were mandatory though.
'Road Tax'. Cyclists are tax payers the same as everyone else and therefore do contribute to the upkeep of the roads. Car/Van/Truck drivers fairly pay extra because these significantly larger vehicles occupy most of the road and indeed are more or less the only users of the 'open road'. Cycles are largely confined to the urban environments (although obviously with the exception of the minority road cycling community.)
'Cycle Superhighway'. STOP. Can we please end this madness immediately. Why should bikes be confined to a narrow path where you can't comfortably and safely overtake other cycles, and on a painted blue surface which becomes slippery in wet weather??