Now look at the all the top students in India. I bet over 90 % of those end up in either engineering or medicine. India has no good philosophers, sociologists, psychologists, anthropologists, etc..
A figure of 90% again looks way too wayward, please when you make claims, back them up with facts, or it's a vague discussion. Claims backed up add value to a discussion.
You are missing out on stuff like architecture, management, law, civil services/allied services, computer sciences, fashion designing, micro biology, finance, accounting, statistics, army, research, and a lot more, and believe you me, the top grade institutes in respective fields have the finest with them. Again, the cream gets divided and the bias shouldn't be either in favour of engineering or medicine.
The top rug of the cream mostly stays in India pursuing their studies with the finest institutes in respective fields, the second rug of this cream and the ones with affordability look for educational opportunities overseas with highly ranked universities, not generalizing, but it happens more or less in this pattern. Of the ones going over seas, as per the study by IIM-B,
"Most of the Indians studying abroad are doing so at the graduate level, with the most popular fields being business or STEM-related (science, technology, engineering, and mathematics)." Again shows, of the total, just a part of the majority pursuing engineering and medicine. Though focus being on those 2, but those alone don't add up to make the most numbers, but these students taking up such courses has to do with the perception that the finest jobs center around business studies or the sciences and its affiliates.
I am not able to get the exact numbers for these overseas students, if you can, please do.
About latter part of the point you made, "of no good philosophers, sociologists, psychologists, anthropologists, etc..", one, let's not generalize because there would be some good names in respective fields, the other, a lot depends on the curve at which the economy is in, the kind of opportunities it is springing up the most, and the focus of the government. If we are scoring less quality numbers there, then the reasons ought to be many beyond just the societal pressures.
45% of students are doing Arts?
Most of these "aspiring" musicians/singers/dancers will end up as fast food waiters too.
It's about what's on offer. if 45% of the total seats, or there about, are in arts stream, and not adequate infrastructure gets created for the rest, most would end up with an arts degree.
Today one of our biggest concern happens to be negligible numbers doing their PhDs, but that's because neither the seats are adequate enough, nor much focus of the industry on research. Infrastructure and opportunities it should come down to.