I think the government should play the most part in it, which can be measured as eight out of ten, and individuals play the rest of two on this matter.

This makes sense, but is phrased unnaturally. I would say something like: "I think the government should play the most part. The government is 80% responsible, individuals are the remaining 20%."

Who is Responsible for Healthcare and Education?

No one can avoid the matters of healthcare and education in their life, which canves; these things can even be used to define a nation's degree of civilization progress.

I think this is close to what you're trying to express.

Some people advocate for solo government to be solely responsibilityle, while others argue against it and are inclined to believe that family plays a more important role in this matter.

I think this actually need slightly more work but these changes already make it closer.

However, I personally, I partially agree with it.

More natural

I think the government should play the mosta large part in it, which can be measured as eight out of ten, and individuals play the rest of two on this matter (80% if I had to put a number to it), and individuals should be responsible the rest.

"which can be measured as" is not really great here because this is pretty abstract. The idea comes across but it's just a little bit rough is all.

No one can avoid the matter of healthcare and education in their life, which can define a nation's civilization progress.

This sentence is good... but what exactly do healthcare and education have in common and how do families play a role in healthcare? I'm choosing the read the rest of this as if it's more about education because it seems to make more sense that way.

Some people advocate for solobelieve the government is solely responsibilityle, while others argue against it and are inclined to believe that family plays a more important role in this matter.

This is a bit of a false dichotomy that makes it sound like only two types of people exist. As you say in your next sentence, "I personally partially agree with it," and that shows that a third option does exist, though.

A more precise wording might be "There are people who ... and there are also people who..." and this wording makes clear that neither camp represents all people. But even this wording still feels awkward. Here's what I would say:

Opinions vary on how much of a role the government should play in education, but at the far ends of the spectrum we have a belief that the government is solely responsible for the education of its citizens and on the other end is the belief that parents are the best teachers.

I think the government should play the molargest part in it, which can be measured as eight out of ten, andperhaps about four fifths of the responsibility with individuals playtaking the rest of two on this mattermaining fifth.