Why did we decide to give February just 28 days when lots of other months have 31 days?

This is an interesting question.

The ancestor of the Gregorian calendar was the first Roman calendar which had some differences: it consisted of 10 months rather than 12. In order to synchronise the calendar with the lunar year, the Roman king Numa Pompilius added 2 more months, January and February. 

The previous calendar had 6 months x 30 days and 4 months x 31 days = 304 days. Numa wanted to avoid having even numbers in the calendar, as the Romans were superstitious and even numbers were unlucky. He subtracted a day from each of the 30-day months to make them 29 and since the lunar year has 355 days (or 354.367 to be exact) which meant that he had 57 days left to share into 2 months. 

Hence, he gave January 29 days like the other months and February 28 days since at least one month out of 12 needed to contain an even number of days. The sum of any even amount (12 months) of odd numbers will always equal an even number and he wanted the total to be odd. So Numa chose February to be the unlucky month of 28 days since that month hosted the Roman rituals to honour the dead. Despite other changes in them modern calendar, Numa's shortening of February stayed with us!