NoAgenda,
I agree with fdaxey's comments about the first question concerning fresh air, but have a different opinion concerning your second question.
First of all, the passage doesn't refer to English majors. The "well-rounded man" is a well-educated and fully experienced man. A specialist by definition is limited to a narrow field of interest. How, then, can the well-rounded man be the most limited of all specialists? The irony is only apparent. The well-rounded man is limited by the fact that his goal is self improvement. His "specialty" confines him to understand the world through the "single window" of the self. As the story of the Great Gadsby unfolds the well-rounded "Nick Carraway" proves to be the only character with wisdom and integrity. His life of self-education and self-improvement makes him more "successfull" than the enormously rich Mr. Gadsby. Or as Shakespeare expressed it, "This above all: to thine own self be true, And it must follow, as the night the day, Thou canst not then be false to any man".