This has been fixed in python >=3.9 by the zoneinfo module in the standard library. The solution in >= 3.9 is probably to stop using pytz.
In [1]: import datetime
In [2]: from zoneinfo import ZoneInfo
In [3]: start = datetime.datetime(2011, 6, 20, 0, 0, 0, 0, ZoneInfo('Asia/Kolkata'))
In [4]: print(start)
2011-06-20 00:00:00+05:30
The reason for this extremely confusing behavior is that time zones used to not be standardized at :30 or :00 offsets. Around the turn of the 20th century most of them came into a standard offset. In the example in OP, the timezone switched in 1906. For US/Central, this happened in 1901.
from datetime import datetime, timedelta, date
from pytz import timezone
d = datetime.combine(date.today(), time.min)
for tz in ('Asia/Kolkata', "US/Central"):
while d > datetime(1800, 1, 1):
localized = timezone(tz).localize(d)
if localized.isoformat()[-2:] not in ("00", "30"):
print(tz)
print(localized.isoformat())
print(timezone(tz).localize(d + timedelta(days=1)).isoformat())
break
d -= timedelta(days=1)
That outputs:
Asia/Kolkata
1906-01-01T00:00:00+05:21
1906-01-02T00:00:00+05:30
US/Central
1901-12-13T00:00:00-05:51
1901-12-14T00:00:00-06:00
Pytz seems to just use the oldest offset when it doesn't have date information, even if it was a very long time ago. In some very natural constructions like passing tzinfo to the datetime constructor, the timezone object is not given that data.