I see a lot of sweeping generalizations here. My parents are also stereotypical Asian parents, and they would choose Amherst over UMich. In fact, my parents see Amherst as the best liberal arts college and have a much higher view of it than of UMich.
As for the OP’s post:
- You mention you want to go to business. I would argue that UMich Ross is better for business than Amherst, although Amherst is good as well. There’s far more recruiting at UMich from business companies than at Amherst (of course, that is also partially due to the fact that not many people at Amherst go into business)
- If your parents don’t se the value of LACs, why are they willing to pay full tuition for schools like UChicago and Dartmouth? While they are not classified at LACs, they have similar liberal arts curriculums. Maybe telling your parents this will change their perception of LACs.