Then there's 13 years (or more) of K-12 education that parents get for free. Private, non-sectarian schooling runs a bit over $16K/year (per http://www.capenet.org/facts.html ), or about $200K per child.
You're right, state education is a massive subsidy... to employers, for example, who would otherwise have to provide most of this training themselves. To workers, for example, who would otherwise be trapped in contracts which prevent them from leaving, because otherwise their employers won't be able to offer them that training. To consumers, for example, because if all businesses had to train their staff starting from the skill-level of four-year-olds, there wouldn't be many profitable businesses to provide us with goods and services.
State education is a massive subsidy to everyone. Everyone benefits from an educated populace. For example, I am pretty happy that the people processing my paychecks and handling my finances had 12 years of basic maths education before they started. It's also an inconceivable improvement to my life that almost every book, news article, blog and forum post that I ever read was written by someone who learned basic literacy for 12 years. And I find it very comforting to know that the doctors and nurses who treat me when I need it, got a 12-year grounding in the human body, how living things work, and how different materials and substances can interact. Plus, I doubt I'd have anywhere safe to live if the people who built my home didn't know basic things about, you know, gravity, how humans need to breathe air, and how electricity can be dangerous. Perhaps more appropriate on this site: anyone investing in stock indexes that depend on
the entire country's economy growing, be glad that that economy is powered by people who have had at least 12 years of knowing-their-arse-from-their-elbow classes.
Everyone benefits, everyone pays. No problem. Considering how much of a contribution parents make to those children's educations that we all benefit from, I even think it's perfectly reasonable to add on a few tax breaks for parents.
But... you're arguing that the primary benefit of education is to the
parents, so it's a subsidy to them? At least admit that the
child themselves gets most of the benefit. Whether or not you have children, if you
went to school, then it's not unreasonable that you pay taxes towards schools.