> A normal human would not suspect Jan + 1 month, is any month other than Feb.

Because humans intentionally reduce the precision of their computations to make them easier.

  Today = 2021-08-04

  Next year = 2022
  The exact month, day, hour are all unknown.

  Next month = 2021-09
  The exact day and hour are unknown.

  Tomorrow = 2021-08-05
  The hours and minutes are unknown.

If humans used the same level of precision as computers, they'd run into the same problems. Probable date of birth calculation is an example.