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I would have thought that objective didn't state wrong or right but only gave facts?
Not necessarily.
If you teach people that 2+2 = 5 then it's perfectly objective to point out that 2+2=4 and you are therefore wrong in your teaching. If "2+2=4" is an objective fact then it logically follows, whether explicitly stated or not, that your teaching "2+2=5" is wrong. If you wanted to defend your teaching you'd need to show that you were correct, or that 4=5 and therefore the two statements were equivalent to each other.
If you were teaching that 2+2=5 and someone were to come along and say "I don't know, that doesn't seem right to me" then you'd have a subjective assessment.