The prime factors of 365 are 5 and 73, which means that the only way you can divide the year up into exactly equal chunks is either by having 5 73-day 'months' or by having 73 5-day 'months'. Since the month was originally set to be roughly equal to the amount of time the Moon takes to orbit the Earth, you can see why neither options were very desirable. Then, of course, you have to take leap years into account. So it is essentially mathematically impossible to have 12 months of equal length.

As for why February has so few days, that is a not a question I am able to answer...