Why do top Indian Math grad school students leave for the US/UK?
Disclaimer: I'm European student at decent Math PhD program in the US.

Sorry, but it seems that I'm going to disillusion you...


  Question 1. So, why do these top students leave these exceptionally
  good schools that are at par with the elite US universities for a
  Ph.D. in Pure Maths?


Although I don't doubt that India have a couple of decent universities with relatively strong mathematics department, they are by no means "at par with the elite US universities". If they really were, I would expect crowds of applicants both from prospective grad students and faculty from Europe and North America to study/work there, but in fact there is quite opposite trend. You have mentioned "topmost schools like IISc, IISER's, TIFR", but without prior web searching I have absolutely no idea what all these abbreviations mean. The same true for overall level of Indian born mathematicians -- they are simply not on par with US, France, Russia and UK in math, just check recent and overall numbers of Fields medalists and ICM speakers. Please do not take it like something offensive, but realizing that is essentially an answer to your question.


  Question 2. What is something that Indian grad schools lack when it
  comes to theoretical Mathematics or in general that drives students
  out of India?


Just in my opinion, they lack


Transferable degree recognition and world renowned top notch researchers like I tried to elaborate above, that is crucial for graduate school, because grad school is essentially about research.
Job prospects after graduation. It goes without saying that Europe and especially North America region (US + Canada) have more attractive job market both in terms of available positions, research prospects and salary than India. In general relocating to grad school is easier than relocating to postdoc or faculty position, this is why Indian students willing to have a shot at American or European job market trying to get in local grad schools.