The US has a large problem with people entering on limited term visitor or student visas and then never leaving. While most of those people are harmless, others aren't (including a number of the 9/11 hijackers). By taking fingerprints of all foreigners, those prints can be entered into law enforcement databases if they overstay their visas. I don't really understand why people would have a problem with it. What bad things would having your fingerprints make it possible for a government to do that having the information from your passport and visa forms wouldn't?