In ancient Rome, leap day was on February 24 due to February being the last month of the calendar. The original Roman calendar added an extra month every few years to maintain the correct seasonal changes. The Julian calendar was implemented in 45 BCE, resulting in a leap day being added to the end of February every four years.
In 1582 Pope Gregory XIII refined the Julian calendar with a new rule that a century year is not a leap year unless it is evenly divisible by 400. The introduction of the Gregorian calendar was observed in some countries including Italy, Poland, Portugal, and Spain. The conversion took longer for other countries such as Great Britain (1752) and Lithuania (1915).
You start with the reference to the Julian calendar and then look for more information just like I did with the various links provided therein on the page. After reading further down the page from the information regarding seasons and the Julian calendar, I see a link entitled
About Leap Day - Feb 29th. If you weren't so spoon-fed, you would have done the same thing and learned what you were asking as it's right there as to how it originally came to be at the end of February. Simply because at one time when leap years were first being realigned, February was the last month of the year. So, it has remained there ever since.
So, in answer to you original question: Why February was chosen for leap year adjustment?
The obvious answer is that it was the last day of the last month of the year.
Apology not needed.