Rhetorically and logically speaking, things are not divided into truth and lies. Some things cannot be "quantified," meaning they can't be measured or weighed or counted. They are nebulous and vague. They might involve feelings or beliefs or trends or opinions that won't hold still even if someone finds a good way to measure them. Some things can be weighed, but it's hard to build the scales. Some things could be studied or researched, but the odds are high of finding botch-job "reports" and "evidence." Bad research is all around us. Good research can become outdated, or be defined, later, as not-as-good-as-once-believed.
Don't plant your feet solidly in the flow of ideas, or you'll be knocked on your ass. Accept the fact that "truth" flows and changes, so that real life and thought won't upset you. Instead of making absolute statements about what is, concerning any field of study, talk about what is currently believed. Plan on things changing and you will be ready to learn happily as they do change.
When you're considering a statement, maybe it's an opinion and can't be proven. Fine. Set those aside for now.
If a statement can be proven or disproven, it could be a fact, or it could be a fallacy, or it could be an outright lie. What would the difference in those last two be? If a "fact" is wrong, then it's not a fact. If it is innocently wrong it's a fallacy right away. If it used to seem right, but the evidence and bases of the beliefs supporting it changed, then it becomes a fallacy—false without the intent to perpetrate a falsehood.
Then there are lies. Lies are statements made by people who know that what they're saying is untrue. Or occasionally, I suppose, they are reclassified as fallacies created by people who aren't sure what is true and what is wishful fantasy thinking. (Kind of the "insanity" subgroup of liars.)
I'm sorry people and advertisements and news stories and magazine articles and blog posts don't come with guarantees or certificates of authenticity. What you need to do with and for your children is to practice sorting through and discovering what will help and what will hurt, what is to be trusted and what is just noise.
Without becoming too critical or cynical, maybe consider, with your children sometimes, changes in knowledge (the platypus, Mars, Pluto, leeches, volcanic activity and virgin sacrifice compared to global warming's medicine men; anything smaller than an atom?), or geography ("Four Corners" has been in the wrong place all these years; the U.S.S.R. is still on maps in some public places) or spellings ("plough" or "plow"? wooly or woolly?).
Play lightly with these ideas. There's no advantage to getting huffy or angry about it. Just see it as the reality it is. People learn. People change their minds. Knowledge grows. Evidence is reclassified. Language is alive. People who are alive are changing and learning. You can resist that or you can ride it with gusto.
I added two paragraph breaks when I moved it.
Other interesting logic moments from the people who made this video.
Josh Groban Backstage (Josh Groban visited, to play himself)
My favorite of all, called Salesman which contains the important question "A real penguin, or a pet penguin?" What if you knock on the doorbell? What if you see so much money?
Facts change; knowledge grows
Logic and Parenting, by Joyce Fetteroll