I should clarify that I am not now, nor have I ever been in the past, Yeshivish/Haredi. My observations and conclusions are solely those of an outsider looking in.
My perception is that there is far less room in the Haredi world for a precocious, curious teenager who is developing a sense of self and what interests him in the world to explore those interests. Where a Modern Orthodox teen with a budding interest in science, art, letters, or any other discipline would be encouraged to develop his talents and pursue his interests in *conjunction with* his devotion to Torah and mitzvot, the similarly curious Haredi teen is not afforded such an opportunity. For those teens who find their thirst for knowledge slaked by delving into the words of Rishonim and Achronim, eschewing Shakespeare, Twain or Einstein may not feel like any kind of sacrifice. But for those who have a passion for “chochmas umei ha’olam,” being taught that devoting time to acquiring knowledge of the profane for reasons other than parnasah is somehow incompatible with being frum can lead to a strong desire to free oneself of what may feel like an overly oppressive or stifling theology. And if, as a teenager, you don’t have the freedom or wisdom to realize that that kind of yeshivish mentality is more hashkafic than it is halachic, you might well end up rejecting Yiddishkeit altogether.