Who said the shove caused an automatic death sentence?
The shove initiated the fight, a fight that continued after the shove. At some point in the fight the officer felt justified in using deadly force. There was nothing automatic about it.
I think that there is a considerable percentage of the population that just doesn't possess the critical thinking skills to connect those dots you laid out in this post or that they are just not inclined to do so. Either way I personally am really tired of this bullshite and it seems it's only getting started.