For example, you leave your username on every comment you make here, but I will never have a clue who you are unless you say in a comment with your username attached.
And after you do that, you will never be anonymous again.
It may seem reasonable in this airport scenario, but the reason people are resistant is because they fear creep. That by giving up fingerprints in this situation, people will eventually be expected to give up private info in more situations.
It is paranoia, sure – if you're not doing anything wrong, what do you have to worry about? But what happens when the definition of wrong gets changed?
Edit:
And it's not like you say at the end: you will still have to take off your shoes. The fingerprinting isn't for better security in terms of safety: it's to make sure international passengers aren't getting on domestic planes – which is only a problem because of the airport's bad, unconventional layout that doesn't separate domestic and international travelers.
A trade between privacy and convenience is one thing, but this isn't even a trade.