What the law says is that you can't shoot someone just for pointing a weapon.
If police can legally shoot a civilian for pointing a weapon, than any civilian could then legal shoot police when they point a weapon.
Police can NOT have superior authority to anyone else, because it is the inherent rights of all individual that is the ONLY source of ANY authority at all in a democratic republic.
The mistake is to believe that since government has authority and hire the police, that then police are a higher authority than average people.
That is not at all true in a democratic republic.
The reality is that since the public create government, then government is below the people.
And then since government hires the police, the police then are 2 steps lower than the population as a whole.
Since police also are average citizens, they do then also have the same right of defense as anyone, but no more.
They have no more right or authority to pull the trigger than anyone does.
The risks they face is why they are paid more.
They can't then start shooting people because they no longer want to accept the risk they choose to take money for.
What police SHOULD do is not to shoot, but to take cover.
They should be acting defensively, just like everyone else.
They do not get the right to murder people so that they can just stand there in the open and pretend it was not their fault for getting into a risky situation.
Let me give you some advice: Never be a lawyer.
The police (and we armed citizens) have the right to use deadly force if we believe that we (or others) are in jeopardy of serious bodily harm or death. The attacker need not even be armed. For instance I'm 60 years old. If three muscular guys in their 20's are coming after me in a violent way, I have the authority by our government to use deadly force. If I kill one or all of the attackers, it's totally legal for me to do so.
And no, if a police officer pulls his gun out on you, you do not have the right to shoot him or her, no more than if you fight him while being placed under arrest. You do not have the legal authority to place somebody in handcuffs, put them in your car, and drive them to jail. That's called kidnapping and you could end up in prison for 20 years.
Police are not average citizens. They do have special authority to enforce the laws of their city, state or county. Citizens by law must comply with their demands because we give them such authority.
Police have ZERO additional authority over any average citizen in a democratic republic.
You say, "I have the authority by our government to use deadly force", and the problem with that is in a democratic republic, government is NOT at all a source of authority, and can not authorize anyone to do anything.
Sure a cop has a right to defend himself and others, but that comes from his own inherent right of self defense.
It does NOT at all come from government, nothing can or does come from government, and if anyone ever does try to establish government as a source of authority, that would be treason.
It is foolish to claim that everyone does not already inherently have the authority to handcuff and jail anyone suspected of a crime. Police have only existed about 120 years, so what do you think people did before that?
Clearly ordinary people have been arresting people for centuries, and it still happens every time a crime in progress is prevented by average citizens, before police arrive, if they ever arrive at all in some remote rural area.
Police can ONLY be average citizens.
There is absolutely NO way they can ever be anything else, in a democratic republic.
Sure they have guns so can start to claim additional authority illegally, but then it is time to string them up form the lamp posts, because they will have destroyed the democratic republic and be trying to implement a self authorizing autocracy.
Autocracy - Wikipedia
If you think about it for even a second, you will realize how foolish it is to claim, "Citizens by law must comply with their demands because we give them such authority."
In a democratic republic, the ONLY source of ANY legal authority at all are the inherent rights of individuals. We can delegate that authority to someone else who is hired to protect our rights for us, but clearly no one can delegate any authority they do not themselves already possess. And they can not lose that authority by delegating it to someone else to use for them. How could we as average citizens, authorize police to ever arrest, shoot, or do anything that we can not already do ourselves? Clearly we can not. So then anyone claiming police have any superior authority at all is way off track and lost sight of what a democratic republic is or even can be. The best you could possibly claim is that in order to reduce the abuses of lynching, that average citizens should defer to police when ever possible. But clearly that almost never comes up. Police almost never catch a criminal in the act. It is almost always an average citizens who does that.
In short, if we can not shoot a suspect how points a weapon at us, and we instead are required to retreat and seek cover, then police must also. Police can NEVER have any addition, special, or superior privileges or authority. It is not possible, in a democratic republic.