Frank, it's about two people having the same birth day, not *what* the day is. And the problem is set in a betting context, ie. what odds you have to win a wager.
Presumably, in a group gathered together, chances are high they are from the same geographic region thus sharing the underlying distribution of births. If this fails, adding more people will cater for any inconsistency regarding the initial assumptions.
Next time you go to a party or meeting of some kind comprising say 20 people or more, just try. I bet you will be surprised.