Your statement has a nice ring to it only because it takes advantage of the very confusing English word "free". In the "free speech" context, it's free as in liberty. In the "universal, free education" context, it's free as in beer; the implication being government funded and managed (and mandatory, implied by "universal"). So while your statement seems to be all about freedom, it's really about predicating one freedom on the restriction of another.
Here's how I would rephrase your statement:
"It's a mistake for the government to let people speak freely before they have been educated by the government."
Depends on who gets to choose the curriculum...don't assume it's people you like or fundamentally agree with.
And, if you do put hard limits on the sort of things that should be taught - and from what perspective - then it really sounds like you're saying that in order to have free speech, people should be taught to agree with you.
Edit: to be clear, I like both ideas. But coupling them, saying we shouldn't have one without the other, is dangerous.
