Can 16 and 17 year-olds vote? No, they can't. So, why should they be allowed to register to vote?
Another thing about why it's important for 16 and 17 year olds to be registered to vote:
Voting registration, unless it's automatic, takes time to be approved and logged into the database.
So if your birthday is, say, November 1st, and your election day is November 4th, and your state doesn't have automatic voter registration; registering to vote on your 18th birthday doesn't necessarily mean your registration will be processed by November 4th.
So that's why you need to register before your 18th birthday.