Microsoft Excel keeps calling me a liar

I have a spreadsheet where I keep track of the birthdays and current ages of my family members. For example, my dad’s D.O.B. is 6/9/34. He is 91 (he’ll turn 92 this June) – but Microsoft Excel keeps insisting in the “Age” field (B6) that he’s 89. The formula I have in that cell is as follows:

=DATEDIF(B6,TODAY(),"Y")

(Note: Cell B6 is formatted as a Date. I changed it to General and then back to Date and it made no difference.)

Any ideas?! I’ve been sober for 19 years and that number is gonna change to “about 30 minutes” very soon!

Thanks