Since about age 12 I have considered myself a "philosopher" much to the universal and monumental irritation of adults (interpret quotes around 'philosopher' as you will). Peers were entirely okay with this and were often intrigued. It's fascinating how many present thoughts and opinions date back to those times. My subsequent scientific profession emerged from this, curiously enough.
I was a voracious reader, but missed out on valuable other exposure -- such as "Philosophy Talk" which was unfortunately lacking back in those old days!

I would strongly encourage philosophy courses at multiple points over the course of an education. I would just as strongly encourage psychology education for every young person.
The inscription at the temple of the Oracle at Delphi said "Know Thyself". That sums up a lot of ancient philosophy and also is the mission of psychology.
Both promote critical thinking skills.
If I had to choose between philosophy and psychology I think I'd have to go with the latter if it helped give young people some insight into why people feel and behave as they do and the pernicious influence of cognitive biases.
Poor Richard
Poor Richard's Almanack 2010

As a contractor, ethics constantly come into play in my job as owner of the company. It would be very easy to not do things right and cover them up. As a responsible person, and contractor, I believe that doing the right thing is the right thing. at http://www.dreamworksremodeling.com that is the only way we do our contracting work. We also use a majority of the skills taught to us in school, including Geometry and of course English (my weak subject).
Les

To your quote: "Of course, I don?t want to deny that philosophy has to be used carefully and that it can be dangerous if used wrongly. Done wrongly, philosophy can be highly corrosive to one?s life. It can lead you to doubt everything. It can cause you wonder whether life has meaning, to question your religion, your country, your parents, and even your teachers."
Umm, yeah! We do want people, young people included, to self examine their religious and patriotic beliefs; as an exercise and because we do not want them to listen to bad arguments for: going to war, making decisions about sex and birth control and many other examples. And I, as a parent, fully want my child to question me if I attempt to lead him astray and into unreason.

What you say: "Done wrongly, philosophy can be highly corrosive to one?s life. It can lead you to doubt everything. It can cause you wonder whether life has meaning, to question your religion, your country, your parents, and even your teachers. Do we really want to cast the young out onto the sea of philosophical doubt and uncertainty? Don?t we want to teach them to how to thrive and succeed in the world? To do that, they sometimes have to accommodate authority, not question it or reflexively rebel against it." I find it the most agreeable part & very conservative at that. Nevertheless, as 'Devil's advocate' (Or Devil advocate) I would say that it is not altogether bad to question life, catholicism, country et al. But KNOW HOW TO QUESTION. That would be the difference between common rebellion & crabby bickering and a philosophical stand. That is, avoid the problems of young (and also problems of older, which are no better): without conformity at any price, without presumptions, without superb pride. Young try to be & think like old and viceversa. The best example is Socrates. People won't burn you if when young you rebel and are against all, because you are young: you are entitled to be mistaken. It is when a serene, calmed but nevertheless reasonable critique is done when they will burn you, be you a child or an old man. Or maybe just give you a treat of a Hemlock cocktail. ¡Good (hem)lock! Life is to ask about things. it is not easy to do, but it doesn´t need to be done unpolitely and gross. Diogenes was a sage IN SPITE of his uncouthness and bad manners. Much I prefer Leibniz, Aquinas, Hume and others. Their humble deaths are an example. Knows to die he who has known to live.

Socrates the philosopher was concerned with Truth. Truth implies, like, avoiding falsehoods, explicit or implicit.
Now, Stanford has a reputation for...Nepotism (ie letting students in who are underprepared, but who may have financial or familial connections which ...allow them to be admitted) .
Nepotism involves falsehood (at least implicit), even of an egregious sort (and for that matter, the ancients opposed oligarchy...a classification which Stanford might fall under).
Thus Stanford does not uphold the teachings of Socrates
QED.
:|

To Freedom
I can see that One day very soon the lessons of truth will supersede or rise above all others, especially those uncertain lessons of theories or faiths that have led us so terribly astray. And rather than the truth showing us The Way to the Promised Land, we will become it.
Simply beautifully and truly just One,
=
MJA

Socrates was executed for corrupting the youth in America, youth below college age are usually not exposed to philosophy in the classroom. Is philosophy all that dangerous? Should it be taught to teenagers?

Regrettably, I have had little interaction with modern day youth, so I am ill-equipped to opine much on the pros or cons of exposing them to the intricacies of philosophy. I can only comment on my own OEOs, regarding my own philosophical evolution. (OEOs=Observations, Experiences and Opinions) Like one or more of your other commenters, I must have fancied myself a philosopher early on. I did not know that my thoughts about certain things might fall under some named category. Philosophy was not taught in either primary or secondary school and would not be addressed formally before university study.
Mostly, my thinking and actions vis-a-vis, right, wrong, good, bad and indifferent got me into trouble, with peers, superiors or both. This happened to anyone who thought and acted differently from the mainstream.
I abandoned much of this aberrent thinking and behavior, and have only re-embraced it in the last ten years or so. I am happy to have done so and hope that something I say, between now and the entrance to eternity, will have some relevence.
There is nothing corruptive about philosophical thought and discourse. But it will not buy food or pay the mortgage. And, if history teaches us accurately, it will not save the world from itself. It might encourage some of us to regard others with more respect and compassion. Perhaps this is all it was ever intended to do. If it was intended to do anything at all.

Philosophy encompasses many subjects. Some of the topics are very relevant to the youth such as logic, ethics, environmental and political philosophy. I believe also that studying the history of philosophy captures the history of ideas and may broaden the horizon of the young and their openness and flexibility.