Creating a Google account is becoming more and more complicated. Until now, when created a Google account in the U.S. required entering birthday. But, it is 'no longer limited' to the US and the features is now rolled out worldwide.
If you're younger than 13 years old and you enter your real birthday, you'll see this message:
"Google could not create your account. In order to have a Google Account, you must meet certain age requirements. To learn more about online child safety, visit the Federal Trade Commission's website."
Children's Online Privacy Protection Act makes it difficult to collect personal information from children under 13, so that's probably the reason why Google decided to prevent these users to create an account. For example, Google would have to "obtain verifiable parental consent from the child's parent." That's not the case when your school created a Google Apps account for you, since the school has to obtain parental consent.
It's also interesting to note that you can't even edit your birthday from your account and that Google deletes the accounts of the children under 13, unless they provide a way to show that the birthday is incorrect. From Google's FAQ:
You can re-enable your account by following our instructions to confirm that you are old enough to have a Google Account. You will see these instructions when you attempt to sign back in to your account. We currently offer two ways to confirm your age:
1. Sending in a signed form via mail or fax with a copy of your current, government-issued ID showing your date of birth, or
2. Performing a small transaction ($0.30 USD) on a valid credit card.