Regarding the Jewish educational system, I did not have the opportunity to attend yeshiva (and of course not BY) but I have noticed that most yeshivot do not teach kol haTorah kulah. As a result, many graduates are unprepared to deal with the challenges of modern society — and not because of inadequate prep in math, science, or history.
As an example: Many graduates of the Jewish educational system who become disillusioned with Judaism end up seeking out Eastern religions as a reaction to the perception that practicing Judaism is about extreme behavior. When I meet them I point them to the section of Rambam’s Hilchot Deot where he brings down as binding halachah that one must pursue moderation in everything with the exception of the humility/arrogance spectrum. Not one of these off-the-derech folks had ever heard that.
Another example: While the Torah faces no challenge from science, those who don’t understand either or both sometimes think that there is one. Again the Rambam has an approach, not often taught, that addresses this adequately for most.
A third example: Many midrashic and aggadic texts seem fanciful and bizarre on first reading. The approach of Rabbi Avraham ben HaRambam, printed as the intro to the Ein Yaakov aggadic compilation, is an approach that can be used to address this while preserving respect for the text and the authors. That may be why the publishers of the Ein Yaakov put it there! Ramban also clearly agreed with this approach — see his comments in his recording of the Disputation of Barcelona. For difficult Torah narratives examples of Rambam’s approach in his Guide to the Perplexed can offer similar solutions.
A fourth example: As we approach the day on which many observe Yom HaShoah we face the very painful question of how HaShem could allow such horrible things to happen to so many good people. There are of course many answers, some of which will be more satisfying than others to different people. Rambam again has an approach that in the past was more popular but has fallen out of favor, in which he restricts Divine Providence to groups rather than to individuals.
Now, many will find this rationalist approach based on Rambam and others with a similar machshavah cold and unappealing. That is fine; they should follow a different approach. The actual number of ikkarim in Judaism is quite small: 13 according to Rambam, 6 according to Crescas, 3 according to Albo. But it should be made available at least to students for whom it is necessary! And all students should understand that it is a perfectly acceptable hashkafah that was held by some of our greatest sages.
In two of the works of the great frum novelist Herman Wouk (still alive at the age of 97) there is a brilliant yeshiva student who at the age of 15 has a crisis when he concludes that Shedim (demons) can’t possibly exist; that they don’t make any sense. Because of this doubt he is expelled from the yeshiva and he goes WAY off the derech. A good rebbe would have congratulated him, pointing out that while that is not the majority opinion, it was the conclusion that no less a figure than Rambam came to!
As you probably guessed, I do find Rambam’s approach to many aspects of Judaism quite appealing. There are other approaches of course, and the entire spectrum of such approaches should be made available to students as appropriate. This is not my original opinion, it was originated by someone far, Far, FAR more brilliant then me, Shlomo HaMelech:
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(Mishlei 22:6).