I don't begrudge that opportunity to anybody. I don't mind paying taxes for the military because the purpose of the government is to secure our natural rights and that is what the military is hired and trained to do.
Schooling is NOT a natural right. One cannot have a natural right to that which is produced by other people: that is slavery.
Certainly taxpayer funding of military training and education should have a positive effect on society
Military education and training is for the purpose of defending the country. Any ancillary benefits to members of the military or society at large are immaterial to its purpose.
The exact same case could be made for public schools
No it can't. You would have to demonstrate that taxing people (taking away their property; denying them the natural right to own that property) for education in general is for the purpose of securing some identified natural right.
I'm not against the practice in principle, because someday, I'm going to hire those kids, and the better educated they are, the more productive they're going to be. Those that don't come to work directly for my company will be providing the goods and services that directly or indirectly, impact the quality of my life.
So is that your political principle? It's okay to take peoples money away along as the goal is to make someone "more productive" or "positively impact your quality of life? The principle I reference was unanimously agreed to in 1776. Yours sounds like it comes from a quasi economic analysis published by Psychology Today.
From a practical standpoint, educational improvement requires two things:
a) Parents must pay for their children's education.
From Milton Friedman's four ways to spend money
Anyway, let's begin with the first item. When you spend your own money for yourself, the tendency would be, which is true all the time, you want to have the best services and goods in exchange for every cent you have. Meanwhile, what is 'own money'? In practical sense, an equity, an asset, a penny that does not belong to anybody but you is what we call "own money". It is sometimes a proceed for yourself derived or earned while doing some risk, like going out for work everyday. Because of that, having the knowledge that you spend substantial effort to acquire it, it is somehow unavoidable that your mind requires the maximum satisfactory return for the least possible amount of money you can shell out. You want to eat the most delicious food your available money can buy, the best clothes for yourself at a discounted rate, acquire the highest rebates, maximizing the rewards you earned, etc... (highest quality for least cost)
b) Fathers have to raise there children.
High School Dropouts. 71% of all high school dropouts come from fatherless homes (National Principals Association Report on the State of High Schools.)
Educational Attainment. Kids living in single-parent homes or in step-families report lower educational expectations on the part of their parents, less parental monitoring of school work, and less overall social supervision than children from intact families. (N.M. Astore and S. McLanahan, American Sociological Review, No. 56 (1991)
Aggression. In a longitudinal study of 1,197 fourth-grade students, researchers observed "greater levels of aggression in boys from mother-only households than from boys in mother-father households." (N. Vaden-Kierman, N. Ialongo, J. Pearson, and S. Kellam, "Household Family Structure and Children's Aggressive Behavior: A Longitudinal Study of Urban Elementary School Children," Journal of Abnormal Child Psychology 23, no. 5 (1995).
Achievement. Children from low-income, two-parent families outperform students from high-income, single-parent homes. Almost twice as many high achievers come from two-parent homes as one-parent homes. (One-Parent Families and Their Children, Charles F. Kettering Foundation, 1990).
I'll align my thoughts on the matter with James Madison.