Sharply focusing on math and science, and then aiming to get into an "old" profession like being a doctor or lawyer, prevents the child from ever exploring or even considering other possibilities.That's exactly the point. They fear that their children will pursue one of those other possibilities the way you or I would fear our children becoming drug addicts. I don't think it's restricted to East Asians; it seems consistent among recent immigrants. I mentioned to a friend from Iran that I had high LSAT scores and could have gone to law school -- I didn't even say a good law school -- and she was astonished. To her, the higher income and prestige of being a lawyer was decisive; it was bizarre that I chose a lower-paid path that resulted in me existing beneath lawyers in the social pecking order. How could I choose to make less money, live in a smaller house in a less posh neighborhood, drive a cheaper car, and go on less lavish vacations?
High-paid professions with stable demand and high, meritocratic barriers to entry are ideal vehicles for recent immigrants, whether they want to ensure their class (if they come from an upper class in a society where falling out of the upper class is catastrophic) or their financial security (if they come from a country where economic existence is precarious and subject to great disruptions.)
Upper-middle-class Americans are a little weird in that we are just as obsessed with class as anyone else, yet we often subordinate class to lifestyle factors when choosing a career. In fact, unlike upper-class, lower-class, or most other middle-class Americans, we are stuck in a kind of catch-22 where it is considered gauche to show concern for maintaining or improving our class status. We also sacrifice security, but I don't think it is conscious: we just can't viscerally comprehend economic insecurity. To my friend, I shrugged and said, "I wouldn't have enjoyed being a lawyer. I might as well choose a career I enjoy. After all, no one is starving." I never had any artistic or musical interests, so my blasé attitude toward class was never tested by the prospect of a sub-middle-class career, but I never questioned it when it came to opportunities to move up. Doctor, lawyer, meh, doesn't sound fun. That attitude horrifies many immigrant parents.