My teacher wants to know what is special about 59 1/2

It's an interesting question, and I'm not sure there's a definitive answer. However, one theory is that it's a way of relating "insurance age" to your actual calendar age. One method that insurance companies have used to determine your age on any given date for acturarial purposes is to use the "nearest birthday" - meaning if you are closer to your 60th birthday than your 59th, you are considered insurance age 60. For example - if you were born on August 1 1950, they consider you to be insurance age 60 starting on Feb 1 2010, and you reach insurance age 61 on Feb 1, 2011. So, assuming the 401(k) and IRA regulations were written using this method from the insurance industry, anyone who is calendar age 59-1/2 by the end of December has reached insurance age 60. Hence, allowing those who reach age 59-1/2 by the end of the calendar year to take a penalty-free withdrawal is equivalent to allowing anyone who reaches insurance age 60 in the calendar year to do so.