Let's extend this to how you might notice a bad representative of these groups on the roads. Suppose you are going out on a trip, which for simplicity we'll say is a straight line down one road. Let's also suppose that at the start of this given trip there is one bad driver and one bad cyclist out on the roads. If you are in a car, the two most likely ways you will see the bad driver is either by passing in the opposite direction (which is usually done lawfully) or by passing in the same direction (which is virtually impossible on most roads that also share space with cyclists). The odds of seeing the bad cyclist are similar if the cyclist is on the other side of the road (again, you would pass going in the opposite direction), but the odds of seeing the bad cyclist if this person is on your side of the road are almost entirely the opposite of seeing the bad driver - it's virtually guaranteed that a driver will pass the bad cyclist at some point. In other words, the difference in the two scenarios is that although the odds of seeing the bad representative is about the same in terms of passing in opposite directions, the odds are virtually opposite if you are on the same side of the road - drivers and cyclists will see each other in passing, but not their own.
This doesn't guarantee that each side is only going to notice bad behavior from the other. My point is more that by seeing a larger proportion of the other group, you are also more likely to see the bad representatives from that group, which may lead you to conclude over time that the majority of bad representatives are from the other group. I don't think this conclusion is true, but I think the thought process is entirely logical (it's just statistics), and I bet many are making this error when they air their grievances about drivers or cyclists. In fact, my experience suggests drivers and cyclists travel safely at almost all times. However, I don't think the fact that majorities of both groups travel safely is the reason why there is this tension between the groups, nor do I think ensuring both sides acknowledge the fact would diffuse the situation.
The problem of one side finding fault with the other (or more precisely, airing grievances about the other side) is one fueled by perception, and I think the perception is based on an accumulation of the statistical effect described in the prior paragraph. If you ask the average driver about cyclists, the odds are good that you'll hear a long list of transgressions committed by some cyclist or the other, but the unstated fact is that these transgressions are a composite story accumulated over many trips. The same applies in reverse - I regularly cycle for half an hour without seeing a single bad driver, which means I can encounter hundreds of cars without the thought of a problem, but I do have a long list of serious situations where I believe a driver was at fault. Of course, this list is one accumulated over six-plus years of rare but incredible near-hits (not sure why the common expression is "near-miss", since that implies a hit). If we think about it using the outline presented earlier, it's all entirely explainable - all the drivers on a given road barely interact with each other, but they pass every cyclist on their side of the road; the cyclists basically ignore each other, but every car on their own side zooms past at some point.
What this means is that relying on drivers or cyclists to testify as expert witnesses against the other side is a nice way to collect aggrieved anecdotes, but it's not a reliable way to measure all the evidence since the facts of traffic patterns ensure a biased perspective. After all, if we assume that drivers and cyclists commit transgressions in equal proportion, then the fact that a cyclist sees more drivers than cyclists ensures that their observational evidence will irrefutably conclude that drivers are almost always at fault. The process of jury selection comes to mind, where a court of law prunes potential jurors from the pool for the smallest possibilities of bias ahead of hearing the case. If a similar standard were applied in this example, then it seems to me that we would rule out having a driver or a cyclist speak against the other side given the likelihood of experience creating bias - not because the cyclist would naturally favor cyclists, but because the experience of a cyclist naturally exposes him or her to driver errors while simultaneously hiding instances of cyclist error. It's not quite that one side or the other is incapable of making a balanced case, but more so the simple fact that being in one group or the other effectively rules out the possibility of noticing problems on the same scale within your own group as you naturally would in the other group.
There is an open question of how to best determine the reality of our roadways. If drivers and cyclists are equally incapable of presenting a balanced perspective, then whose voice should be amplified in the discussion? If we must hear from each side, then the instinct is to look for some kind of compromise, where voices from each side can offer basic changes that could diffuse the ongoing hostility and begin rewriting the narrative. What if each side started from a premise that the other side likely held a better perspective in at least one specific area, then committed to implementing a change that addressed this primary grievance? Perhaps drivers could stick to the 25 MPH speed limit in these two cities while cyclists could stop at red lights for once (which is kind of like the same thing, if you consider that a red light is basically a temporary change in the speed limit to 0 MPH). If things go well in the first year then we could try it again in the next, initiating a routine of incremental improvements supplied by one side for the other, all with the goal of slowly making the roads a safer and more accessible public space for all.
But maybe the better answer is to look back at that juror example and consider what the equivalent would look like in this situation. It seems to me that finding someone who lives in both groups would make for the right person to provide a balanced perspective. This person, ideally, would be the sort who makes trips from behind the wheel just as often as making trips while gripping handlebars. I've only had a few instances where I could gather perspectives from such people, but early returns imply a trend. There is a reality about cars and bikes that becomes all too evident when you share enough experiences - drivers and cyclists alike understand that a car is much more likely to kill them than a bicycle. Even in the cases where this type of person feels that cyclists have more to answer for in terms of error frequency relative to drivers, there is always a limit when the equation is rebalanced to account for the weight of each transgression, with the result resembling the way one acknowledges the difference in the relative threat between a flamethrower and a cigarette lighter - both can burn, but such an observation omits the relevant detail.
A piece of metal, weighing nearly two tons and travelling at 30 MPH, is a little different than a blue cinder block repurposed for the local bike share program incoming at 10 MPH. If you had to make your stand in front of one or the other, which would you pick? I've seen people make that the decision, and they make the same choice every time, demonstrating a certain kind of wisdom about the road that can't be worked out with logic or built up with compromises. Both sides are responsible for fixing their mistakes, but one side's mistakes disproportionally kill the other, and many on their own side as well. It seems pretty clear to me what the reality is on the roads, but some people won't believe it until they see it. I just hope it's not my corpse, tattooed with tire tracks and motor oil, that's destined to be some driver's epiphany.