Look here's the part that doesn't make sense to me: if Brown assaulted Wilson at the car with the intent to kill Wilson, why didn't he finish it right there. Why did he walk or run away at least 30 feet, wait until Wilson got out of the car with his gun in hand and then charge Wilson at full speed as bullets are flying past him? No matter how many times I hear this scenario, I just can't see it happening.
Doesn't it make much more sense that Brown, who was a stupid thug, tried to punch Wilson, maybe even went for Wilson's gun, failed and got shot in the hand, took off and fled, so Wilson got out of the car, yells at Brown to stop, Brown turns around, and Wilson in a state of fury and fear shoots him dead? That's a story I can buy. I don't even particularly blame Wilson (though it would be a wrongful death). But this charging stuff has got to be nonsense.
An alternative hypothesis.
The struggle took place in the car, for whatever reason or on whatever provocation, and regardless of who initiated it. It took place. During the struggle Wilson's gun discharged at least once, and I understand more likely twice. At least one of these shots grazed Brown's thumb and came with some searing hot gunshot residue going into his flesh. Now this likely hurt, was startling, caused both parties an adrenaline rush triggering fight or flight responses which beginning to obviate them analyzing their next moves 100% logically. (Now Wilson's training should have helped with this some, but it is difficult in training to really simulate situations to the point of producing rushes of adrenaline). we need also understand that discharge of a weapon in a car would be incredibly loud, would leave a painful ringing in the ears, and with the accompanying discharge of smoke would be disorienting.
At any rate, brown, being wounded and startled, would naturally, reflexively, begin retreating. It would be less natural for Wilson to immediately pursue, this would have to be a volitional action after some fractions of a second or more consideration.
When Wilson exits the car brown has had whatever time to compose himself that it would take to travel whatever distance he got. I think we all agree this is not a long time, seconds at the most. As for Wilson he is now confronted with a split attention task. Outside the car is not just Brown, but brown's cohort. It seems possible, likely even given common experience that Brown and the cohort were shouting back and forth, I mean brown had just been shot. Officer Wilson may have been directing his attention, and his gun, back and forth between the two as yet less than fully assessed risks. During this process Brown may have seen an opportunity to advance on Wilson. he may have been encouraged to do so by his cohort, egged on as it were.
What we know from common experience is that criminals avoid apprehension. We also know that in fight or flight response scenarios one can turn instantly from the one response to the other. Experience tells us that young men misapprehend their abilities and competencies. Experience, no history also shows that folks will charge at and fight armed Officers.
You are trying to apply logic to an illogical situation involving rage, injury, pain, fear, and desire to escape. The fat man may have decided his best escape is not to run, but to fight. Fat people understand that their running ability is limited after short distances. they are built for charging, not for marathons. For all we know he may have thought the Officer was stunned from his blows and shot. The officer may have been disoriented and staggering.
I am not advocating this position. I am advocating that to dismiss it out of hand may be precipitous and may involve not assessing all the factors. You want to apply logic, but you ignore the human condition, and you forget to paint an accurate scenario, one involving Brown's friend in the picture as well. A person who is an independent actor, who likely was not a silent statue during the encounter, and even had he been he would have still created some split attention tsk for the officer potentially presenting Brown an opportunity for charging Wilson.