Why do some months have 30,31 and 28 days ?

Nobody can give you scientific reason for it but there is a factual reason. First king of Rome invented calendar for the evaluation of time ,which had 10 months from March to December and was based on moon. Obviously this calendar didn't have any relationship with seasons and time of Earth.
Second king of Rome Numa Pompilius deciphered the mistake and made second calendar which had 355 days. He added January and February in it. Both the months earlier had same 28 days but according to Numa which was mythologically unlucky so he added 1 more day to January.This calendar was also not contemporary with the seasons on Earth.
In 45 BC Julius Caesor came and denied the 2nd calendar. Julius Caesor's calendar was known as Julius calendar. This calendar had 365.24 (355 + 10) days with March as it's first month with 30 and 31 days respectively . February had 29 days in this and after 4 year there was a leap year which had 30 days. Later Caesor's calendar named July month for memory of birthday of Julius Caesar which had 31 days and August month is named after the memory of Caesar's nephew Augustus Caesar and it's days to 31 reducing 1 day from February . Remember it. This 365.24 days was very similar to time taken by Earth to take a complete round of Sun .

In 1582 Gregorious calendar was introduced which had January as it's first month and December as last. Later in 1952 it was implemented by US and Bretain in their states , which is worldwide now a days.