Explain how it is "not a fact". Unless you can prove that their beliefs are not true, your belief that their beliefs are not a fact is precisely that-- a belief. Not a fact.
I wouldn't say "merely" a belief. But yes, it is my belief, and this doesn't do anything to discount its value.
No, it just makes your position full of double standards.
OK, let me try giving my analogy again, since it seems to have been ignored:
We base laws on verifiable harm because it's generally accepted to be a bad idea to try to base them on people's individual moralities. Most people can understand and agree with that, even if they have strong personal moralities. It's based on the idea of not imposing beliefs on others, unless there is verifiable support for those ideas that make practical sense.
Using that same thought process indicates we should treat the education of our children the same way. If something has verifiable evidence, as in evidence that can be presented to anyone and agreed upon, teaching it as fact works. If it doesn't have that, but rather is a personal belief, then teaching it as fact isn't ideal.
Basically, in the law we make the distinction between personal beliefs and beliefs that can be agreed upon by everyone. I'm just using that same distinction in regards to how to teach children.
Your analogy doesn't make much sense.
For one, no, laws are not based on things everyone can agree on. This is pretty self evident.
For two, they are more about practicality and effects upon society. It doesn't have much to do with facts or truth vs personal opinion.
For three, determining what should or should not be a law doesn't have much to do with "not imposing beliefs upon others." Not to mention, various laws, both past and present, are very much about subjective morality.
And for four, even if all the above fell in your favor, I'm left scratching my head why we should be basing how to raise our children on how we make laws.