Well, one issue is that there are different date formats used worldwide and there's a risk that the website will accidentally swap the month and date if I simply enter three numbers without thinking about them. mm-dd-yy and dd-mm-yy are both used occasionally.
There are also different calendar formats.
You're unlikely to change your mind about when you were born.
You really only ever need to provide three well defined numbers.
So, why display a calendar?