In today's society, some people think that the families whose children do not attend public schools, should be free of payingexempt from taxes supporting universal education.

"Free from" could possibly also work, but it sounds clunky to me when used with a verb or action.

To begin with, I should say that tax systems differs from country to country, also does thes do education systems.

IMost of the time, in my country, people who pay taxes most of the time don’t know, where exactly their money goes.

You could also move "most of the time" to after "don't know" or to the end of the sentence. In the original position, I was going to interpret the sentence as a statement about people who usually (but not always) pay taxes, but that didn't make sense.

The taxes are collected tofor the government budget, after thatwhich the government decides on where to accumulllocate thoseat money.

"Budget" refers more to the allocation of money itself, so "collected for" makes more sense. But you could also replace "budget" with something else.

The public education system also has its own problems.

For example, it could be money for renovating the school building renovation, or payments to make renovations in classroom, payments for classrooms improvements, etc.

"School building renovation" and "renovations in classrooms" sounds a bit redundant, so I would rephrase it.

In my school days, they even charged us to pay for new textbooks, whicthough I believe is already past itthat that is no longer the case.

As a result, those payments could bring corruption into public schools.

In a good workfunctioning tax system, people know the purposes of payments.

I would also add something before "payments," maybe "their" or "different."

In this situation, people who attendenroll their children toin private school,s see that their money goes to the universal education, which they haderive no benefit from.

In my opinion, these people have their right to not to pay for the part of the system that does not impact on the lives of their children.

To summarize, in different countries social instituteions do not work the same in different countries.

"Institute" refers more to an organization.

In thea well-organized system, citizens should always know where taxes are directed to.

People who attendenroll their children toin private schools, being a small part of the society, and should be free ofexempt from paying for universalthe public education system.

In today's society, some people think that the families whose children do not attend public schools, should be free of paying taxes supporting universal education.

To begin with, I should saymention that tax systems differs from country to country, also does ong withe education system.

In my country, people who pay taxes most of the time don’t know, where exactly their money goes.

The taxes are collected to the government budget, after thatnd afterwards, the government decide where to accumuls about whate those money should be used for.

For example, it could be money for the school building renovation, or payments to make renovations in classrooms, etc.

In my school days, they even charged us to pay for new textbooks, which I believe is already past itno longer happens.

when you say "charged us", that means "we had to pay money", so you don't need to say "pay"

In a good workwell-functioning tax system, people know the purposes of payments.

In this situation, people who attsend their children to private school, see their money goes to the universal education, which they haveget no benefit from.

In my opinion, these people have their right to not to pay for the part of the system that does not have an impact on the lives of their children.

To summarize, in different countries, social institutes do not work the same.

In thea well-organized system, citizens should always know where taxes are directed to.

People who attsend their children to private schools, being are a small part of the society, and should be free of paying for universal education system.