Are you talking about Chinese parents inside or outside China?I guess most parents want their kids to be whatever is the most prestigious. In China the means (or at least meant) engineering, outside china that means doctor or lawyer.
I'd say in America it's mostly just STEM or business/economics, depending on your family background. Business for children of business owners, STEM for everyone else. There's also a clear political divide along this line in oversea Chinese demographics.
Lawyers, although well-paid on the higher-end, carry somewhat of a bad rep of being predatory and unreliable income-wise across the spectrum.