Thing is, your dad is wrong too. And isn't curious. It is possible to know the age of the earth within a pretty decent margin. Assuming there is no answer to a question is just as bad as never asking the question in the first place. "We can't know the answer to this" is an inherently blind notion.
Yes, public school is a mess in some places, but at least it's not teaching people information that is provably false. And really, the problem is mostly public schools in non-wealthy neighborhoods. The upper middle class suburb high schools do a lot better. Poor performance of schools doesn't make the influence of religious fundamentalists any less damaging,