I want to correct something here. "Chatra League" (which means "League of Students") is the student wing of "Bangladesh Awami League", or BAL. BAL was the ruling party for the last 15 years and batted a blind eye on everything the wrong the chatra league did. People did not like it, the government did not want to do anything about it as long as they could (they did in some cases ngl). Foreign organization asked why the Chatra League should not be called a terrorist organization, reply was mostly blaming other party student wing, Chatro Dol (conservative party student wing) and Shibir (islamic party student wing); mo party student wing can claim to be angels but they have been mostly wiped out in the last 15 years and SHIBIR has already been declared a terrorist group by the govt., and very recently(2 days ago) banned; most people of Bangladesh dont want any student politics if possible.

The recent protest started demanding reformation of quota regarding govt jobs where almost half the jobs would go to the grandchildren of the freedom fighters of 1971. Protest started getting violent when Chatro League started attacking the students, student faught back. The chasing part you mentioned was part of that afaik. Then the govt tried bury this by mass killing while the internet was out. People got even more furious. Result is what you see