Is the program not allowing it, or is IRS not allowing it?

For some purposes, your age on December 31 is what you celebrate on your "birthday" of January 1.  For others, at least as far as IRS is concerned, it is not.  See this Revenue Ruling from 2003:

https://www.irs.gov/pub/irs-drop/rr-03-72.pdf 

But that refers to the age of the child who qualifies a taxpayer to claim the credit, not to the age of the taxpayer. 

The rule that "you turn 65 on December 31 if your birthday is January 1" has been around so long, I don't know its source.  I don't think it's in any statute.