Given the benefits of a public school education over private day school education, such as $0 tuition and technology and extra curriculars which many schools do not have, why don't most orthodox American Jews send their kids to public school for their secular education and then hire tutors for Jewish studies? Is this an entirely socio-cultural phenomenon or are there halachic reasons as well?
I write as an Orthodox Jew, a parent and a teacher. The answer is both simple and complex.
First, the money. Yes, public school is cheaper. Can't get around that.
Next however is the contention that Jewish schools lack "technology and extra curriculars" -- this is not true for a huge chunk of Jewish schools out there. From teams to clubs and from iPads and Smartboards to coding classes and Engineering programs and everything in between, many Jewish schools offer curricular and extra-curricular perks on par with non-sectarian prep schools. The education presented is very often top notch and the decision more often hinges on money and not a sense of "you get more at public school."
But beyond the courses and quality educators there is the question of environment. I believe that education incorporates an awareness of religion and spirituality across the board. The integration of a Jewish identity into a young person's identity is a constant and consistent process. It cannot be done in fixed hours on Sunday or in the afternoons without being undone during the class time. Judaism is a life and not just a basic set of rules. The public schools MAY NOT (by law) include the kind of sensitivity to and training in history and ritual that I want my children to have.
Mix in the concern over the potential for conflict (games on Shabbos, treif food at school events, no days off for Yom Tov) and the position you put impressionable children in either having defend/explain their own religious position or be influenced by what they see around them (peer pressure isn't always intentional or malicious), the decision to help nurture a rounded, religious child in a sheltered environment which make them stronger educationally is not an unusual one.
I graduated from public school. My comments are not a result of the caliber of the education or even the environment - my school won national competitions in academic competitions, and was a very clean and safe environment. But I would never think of sending my child to the best public school.
1) - My school (which ended a bit earlier than the schools around it, except for senior early dismissal) ended at 2:30 in the afternoon. Elementary and middle school ended later. That means that you want to now add in the equivalent of a day-school Jewish education (I can't speak for every school, but in my town that means about 5 hours). So this child will be finishing school when most kids are in the middle of dinner. On top of that, a planned double-curriculum will be designed so that homework is balanced for both halves of the curriculum, and the Jewish part of the curriculum could be supplemented at home, whereas a public school will not be factoring in time for another curriculum, and if you want to add on additional study or work, it will be on top of a full curriculum not designed to accommodate such.
2) - The Rambam writes in Hilchos De'os 6:1:
My peers did not have the same values as me. These were people who were legitimately my friends (I was invited to some of their weddings years later), as you would expect to happen with people who are spending hours together every day, and they were having social interactions on Shabbos and Yom Tov, which involved things which were objectively forbidden by the Torah, and I had to just miss out on that part. I had to be in a position where I couldn't be completely "part of the gang" but I couldn't just pretend they weren't my social groups. (I happened to have very good friends who did not make me feel outcast, but that didn't mean I enjoyed missing the parties.)
3) - ולא תתורו אחרי לבבכם ואחרי עיניכם - There are certain things which a Jew is not allowed to see (e.g. a woman's thigh, breasts). The dress code at my school was that a young lady's shorts or skirt had to reach at least below her fingers when they hung at her side. This was made more lenient before my younger sister graduated. A shirt had to have straps, but cleavage and stomach below the belly button was allowed to be exposed. A strap could also go around the neck (i.e. a shirt with a very low or absent back, held up by straps from the front). So hormonal 14-18 year old boys are going to be expected to keep their eyes on their toes the whole day? Additionally, phys-ed is a required part of curriculum in virtually all public schools, and they aren't offering separate swimming hours any time soon. I had to play sports with the opposite gender, and go mixed swimming. I actually had an English teacher who occasionally wore mini-skirts, and it's hard to ignore the teacher.
4) - In the Yeshiva school in my town, the role models for the students are rabbis and qualified women who represent Torah values. The secular teachers are vetted by the school, and are not espousing viewpoints contrary to the Torah. A young mind is especially vulnerable to the opinions of adults perceived as authority figures, and mixed messages are at best confusing for them. My Art teacher was a Jew for Jesus and wanted to talk to me about it, since I was the only one around with a yarmulke. It's hard to tell your teacher (who determines your grade) that his beliefs are heretical and you aren't interested in discussing it.
5) - Public school follows a secular calendar. I had to make up all the work that I missed over a Thursday-Friday Holiday, which is made more difficult when often quizzes and tests are scheduled for Fridays. Tishrei has 7 days of Yom Tov, plus you have to go to school on Chol Hamoed to not exacerbate the issue. Shavuos was always a fun one, since Finals are right around that time. I actually missed the entire review period for AP Statistics because of Pesach. Jewish schools have calendars arranged around the Jewish calendar.
6) - Sticking out is not always easy. Sometimes, it was fun being the only guy with a lulav in his car. But I remember someone loudly declaring in the hallways (in protest of the no head-coverings allowed dress code) "how come he gets to wear one"? (I actually had to get special permission from the principal and show a note to my teachers stating I was allowed to wear my "skull cap.") Another day, there was a kid who followed me down the hall chanting "yamika yamika yamika." I never felt threatened, thank G-d, but I wasn't always so comfortable either.
On top of all of this, for many the secular education is just not important. Your average "right-wing Orthodox" family is objectively more concerned about the par of the religious education, and the secular education is at best a second consideration. Look at many "right-wing Orthodox" Yeshiva high schools and you will see that they, and the parents in many cases, are just not bothered that their children won't be getting in to Ivy League schools. The value system expressed in the question is simply not the correct hierarchy in their eyes.
As a postscript, the challenge that public school poses to observance is not something that we look forward to or take lightly. The fact that it is a nisayon, a trial which tests your mettle, is not something we invite. It's nice to say that we would hope our children will be strong enough to withstand the questions and the tests, but we do not go looking to be tested. The Talmud (bava basra 57b) describes someone who chooses to go down a path on which he knows he will see women immodestly dressed, and describes him as an evil person even if he doesn't look, as Rashi writes:
He is an evil person even if he closes his eyes because he should have distanced himself from the opportunity of a sin. We do not put ourselves into trying situations and hope we do well. Avoiding the test is an objective value, and Jewish schools present that option.
Although America is a much more religious country than other developed Western democracies, the typical social atmosphere among young Americans is extremely secular and often anti-religious. Most of American popular culture is devoid of religion and consistently promotes a social liberalism (indeed, often libertinism) that is at odds with the teachings of traditional religions such as Orthodox Judaism.
For these reasons, it would be very difficult for an Orthodox Jewish child, growing up in a public school with many secularized non-Orthodox friends immersed in American popular culture, to maintain a solid Orthodox hashkafa and remain observant into adulthood.
The available data shows that Jewish children who attend Jewish day schools have a far lower intermarriage rate than children who go to public schools:
"According to a National Jewish Population Survey conducted by the United Jewish Communities organization (2000-2001 survey), more intensive forms of Jewish education in childhood are associated with lower rates of intermarriage in adulthood. Those with Jewish day school/Yeshiva education had a 7% intermarriage rate, as opposed to those with part-time Jewish schooling—meeting more than once a week or once a week—who had 23% and 29% intermarriage rates, respectively."