I just watched the full video for the first time. (Up until now, I've only relied on the clips that were in news shows). The full video is disturbing, but it's worth watching because it makes two things very clear:
1) This wasn't an accident. They knew exactly what they were doing.
2) The bystanders on the street pleaded and pleaded with the police not to kill this man, but the police kept doing it anyways.

In my little video manifesto on anarchism that I made last year, I tried to make the following point: if left to their own devices, people naturally want to help each other.  If you saw a bleeding body on the street, your natural impulse would be to try to save their life.  But it's governments that force people into wars and violence.  Anarchists didn't make the death camps in Auschwitz. Anarchists didn't nuke Hiroshima.  Anarchists didn't ship draftees around the world to kill people they didn't know.  Anarchists didn't bomb Vietnam into smithereens.  Governments do this.
Was that point a little bit too simplistic? Maybe.  I don't know.
But watch the video.  Notice how the natural human reaction of everyone standing on the sidewalk is to want to try to help the man.  But the police, as agents of government and authority, automatically just kill the man, without appearing to give any thought as to why they're killing him.  They just know that they have the power to do what they want, and so they're not concerned about the consequences.
And it's not even entirely a race thing. No doubt the fact that George Floyd is black made him vulnerable, but the lines of racial division are not entirely clear cut. Notice how one of the officers who killed him was Asian American, and one of the bystanders pleading for his life was white.
Rather, the clear division is between those who have institutional government power, and those who do not.
Nor is this a case of "a few bad apples".  Unless you believe that there are only a handful of bad apples in the Minneapolis police force, and it's just a coincidence that in this case all 4 bad apples all happened to be at the same spot at the same time.

There's also a telling line in the video, when one of the bystanders says, "We need to call the police on the police."  It's meant to be ironic, but it illustrates their complete lack of options to resolve the situation.  When the police are killing someone in front of you, what can you actually do?  There's no other authority you can appeal to in order to resolve the situation.  They've been given authority over you, and if they decide to slowly kill someone in front of you, all you can do is beg them not to do it.  And if that doesn't work, then all you can do is watch.

It's worth remembering at this point that for most of human history, we didn't have a police force.  Communities were able to regulate themselves.  Most people have a common desire to help each other.  Watch the reaction of the bystanders.  They're illustrating our common desire to assist someone in trouble.  But what function do the police serve?  To bravely stand on the street corner and stop people from checking George Floyd's pulse? When you give human beings institutional authority over each other,  and when you give humans unlimited power to do what they want, then you're going to offset this natural human impulse for mutual aid, and the result of what kind of society you will end up with is so clear in this video.

If this video isn't the best argument for why people should be allowed to regulate themselves without the police, then I don't know what is.

George Floyd Died After Police Knelt on His Neck During Arrest | NowThis



Addendum June 3, 2020: Further thoughts
We've been so propagandized by everything in our media and culture to believe that we need police.  We've been made to believe that the only thing separating us from savagery is that the police are there to prevent us from all of a sudden turning on each other and tearing each other apart.  This is such an ingrained belief that it's difficult to get people to think otherwise.
It's so easy to forget that police are a very recent addition to civilization.  Certainly the idea of an organized modern police force only goes back to the 19th century.  And communities were able to regulate themselves just fine without the police.

What benefit do we get from the police?  Watch the video, and ask yourself what benefit the police brought to this situation?

And yet, we are against systems, and not men.  When a police officer says, "I saw the video, and I was just as horrified as you were," I think the correct response is to say...
"Yes sir, I'm sure you were.  You are one of the good ones.  But if you weren't so good, then there would be nothing to prevent you from strangling me to death right here in front of everyone, correct?"  I mean, sure, there would be legal ramifications later. (Maybe). But during the moment, what restraints are put on the police officer?  The bystanders couldn't stop the police officer, or they'd be charged with assault or interfering with the arrest.  And again, I'm not talking hypotheticals here.  Watch the video.

Addendum June 8, 2020:
Posted this originally on Facebook, but I'll add it here too:

A lot of people posting on Facebook lately about all the good cops they know. With respect, this is not the issue. The question is not "Are there any good cops out there?" The question is: If (theoretically) one of these cops was not so good, what protections do we have in place to prevent them from killing you in broad daylight?

Addendum June 10, 2020:
I've noticed that some people on the Internet don't understand why the bystanders didn't intervene to stop the police.  This seems to me to be a dangerous misunderstanding about the power dynamics that are actually in play, so I wrote a separate post about it: You Can't Overpower the Police