People have a very difficult time distinguishing between impossible and implausible.
In high school I got into an extended debate with a fellow baseball fan about whether a particular set of circumstances was possible on the field. I argued that it was impossible for a ball to strike the top of the outfield wall without either going over the wall for a home run or back onto the field of play for a hit. It was not possible, in other words, for the ball to hit the top of the wall and then come back down to hit the top of the wall a second time. It simply could not be possible for a ball hit from a great distance at high speed to strike the very narrow top of a wall from a sharp angle of approach (while rotating, by the way) and essentially bounce straight up and down. That would be like flinging a rock into a lake and having it bounce straight up rather than skip or sink. Some laws of physics can't be violated.
Never being the kind to back down (and being friends mostly because we were both awkward nerds) he endeavored to prove me wrong with high school physics and geometry. He put a good deal of time into drawing up a scenario under which the ball could do exactly that – if the wall had exactly x density and was struck at y speed and z angle with the wind blowing inward at b miles per hour, the ball could do exactly that. While not confident in his 15 year old mastery of physics nor my ability to pick out the potential flaws in his argument, I relented. It was not strictly impossible – just highly unlikely.
It has been many years since we spoke, but I bet that my friend and fellow White Sox fan remembered our adolescent dispute a couple weeks ago when, giving the finger to physics and common sense, Adam Dunn mashed a ball that hit the top of the wall. Twice. And then returned to the field.
Some things are impossible; they literally cannot be done, like fitting a square peg through a round hole (provided the width of the square is not smaller than the diameter of the circle, pedants). But most things, even the ones we ordinarily think of as impossible, are merely implausible. This causes a pair of problems that have, over time, birthed a million conspiracy theories and plain bad arguments.
First, people have a tendency to conclude that if something is highly implausible it is not possible. For example, it is quite implausible that on 9-11, three lightly trained terrorist-pilots who had never previously flown real airliners could steer them into stationary targets including the Pentagon, which is less than ten stories (75 feet) tall. It strains belief. The odds against it must be large. But it happened. The Truthers, however, have seized upon the improbability of the chain of events to bolster their argument. Since it is unlikely to have happened, it couldn't have happened.
Second, people tend to do the opposite as well and argue that as long as something is not impossible, it is a perfectly useful explanation of events. And any argument that can't be 100% ruled out is as good as any other, according to the world's most annoying motivated reasoners. For example, oh, I don't know…if it's possible that an unarmed black kid decided to try to get the gun away from a cop – so he could, I guess, kill him? That was the plan? Kill the cop? – then that version of events is the perfectly correct one for people who really want to believe in a chain of events that exonerates the police.
In short, when all available evidence suggests that x happened, the fact that x is implausible is irrelevant. Conversely, when all available evidence suggests that x didn't happen, the fact that x is plausible rather than impossible doesn't bolster the argument. Logic doesn't care how likely or unlikely things "seem."
Is it possible than in a moment of panic, an unarmed teen with no criminal record decided that he would lunge for a cop's gun when the officer told him to walk on the sidewalk instead of the street. I mean, that could feasibly happen. For something so highly implausible to emerge as the definitive account of the events, though, would require a good deal of supporting evidence. When the tale goes contrary to all of the available evidence, its implausibility becomes a serious liability.
You believe that Adam Dunn did something really implausible because I showed you a video of it happening. If, instead, I merely told you that I saw it happen, you'd be skeptical. That skepticism would increase if I couldn't produce anyone else who attended the game and claimed to see it. It would all but disappear if a parade of eyewitnesses contradicted me and said that the ball went straight over the wall. At that point, the only way you would believe that it happened is if you had some unusual faith in my honesty…or you really wanted to believe it.