You shouldn't set a default for a birthday. Just as you shouldn't set a default for:
- Name
- Email
- Credit card number
- Credit card expiry date
- etc.
The line of reasoning goes like this:
Usability
Usability is a measure of performance load, which is broken down to:
- Cognitive load - the effort users expend when perceiving, interpreting and making decisions regarding the next action. Normally meassured in time between exposure to the interface and action onset.
- Performance load - the effort user expend when taking an action. Measured using mouse miles, mouse clicks, keystrokes etc.
So unless some business goals take priority, the a key role of a design (and a system in general) is to minimise performance load.

Social threshold
When making UX decision we sometimes use data or guesstimates as to what percentage of users will benefit from a particular design.
For instance, you may see from analytics that 98% of users has a display size wider than 1200px. So setting your layout width to 1200px may benefit 98% of users, but for the remaining 2% the layout may start stacking, or you can force horizontal scroll - neither is ideal. But all taken into account, it seems a reasonable change to make.
Some set the social threshold to the famous 80/20 rule - if more than 80% of the users will benefit, it's a design worth going ahead with. But, as always, many variables could affect such decisions.

Cost/benefit analysis
Cost/benefit is another commonly employed analysis helping to make design decisions.
If you do set a default date, you will get 'perfect hit' in very roughly 1 in 15000 users (assuming an age span of 40 years). That's around 0.007% of the users.
You may argue that 0.007% is better than 0% (with no default), so lets consider the cost for all the other 99.993% of users:
They may wonder why the field is populated, which could increase the cognitive load a bit. But perhaps the main danger here is security - in the age of cookies, it may appear to some that the form was field previously by another user, it which case some privacy concerns may arise. At any rate, you run the risk of confusing users.

Conclusion
The overall approach to this problem can be depicted like so:

So given the low percentage of those who will benefit from a birthday default, and the potential security and confusing cost nearly all users will experience, this seems like a clear-cut don't provide a default.