> A government can be defined as "a public organization for the systematic and systemic persecution and elimination of minorities"
Yes, but that would be a silly definition; governments rarely persecute as an end goal.
A more sensible one would be: a government is what controls a state, and a state is an organisation with a monopoly of legitimate force on an area of land.
Can you name a government that does not systemically and systematically persecute murderers? Pedophiles? Tax evaders? Drug users? The list goes on. Minorities are not limited to race, gender and the like.
The persecution perspective raises several ideas to the surface that get buried under the monopoly of force definition. The latter is concerned with collection of power, but the former is concerned with the use of power. Further, in countries such as the US, there are numerous arms among the citizens and the government cannot be truly said to have a monopoly of force (disproving the definition at least in part).
To what end is a monopoly of force? There is always a moral judgement in the use of power and always a line in the sand concerning who should be persecuted. Sometimes that line is murderers and sometimes it is homosexuality or saying things the majority disagree with.
Further, the persecution definition is more accurate in that it places the responsibility into the correct hands. Governments are formed by the people who consent to them and have no life of themselves. Even in a place like North Korea, most people endorse a government that most of us find horrible. The position of that line of persecution isn't determined solely by government fiat -- it is a result of the people's consent and inaction.
A government would find catching murderers impossible if the general population did not (as a majority) support and help them. Slaves would not have escaped from the South in any significant number if so many people in the North had not consented. Likewise, lynchings, kangaroo courts, and Jim Crow would not happen if the majority of people had not consented.
Very importantly, this view forces home the effects of intolerance. When a large group of people silence their opposition "freedom of speech isn't freedom from repercussions" they are in fact exercising this exact type of governmental persecution power, but without the tolerance that is otherwise "agreed" upon.
This raises what is (to me) the most interesting argument of all. Speaking of the US. We agree that the government cannot punish people for controversial, but non-inciteful speech. We are the government ("by the people"). We simultaneously agree that we can do the exact opposite in our personal lives and ruin someone we disagree with. This shows our true line in the sand is very much not in sync with the one we voted for and illustrates a very complex, but dangerous cognitive dissonance.
I could go on, but this lens is the most useful one I've seen for looking at how society, morality, and government interact.
The only major dispute between governments is which groups of minorities to target.