Because the basic idea of a no-fly list is an attempt to avoid due process.
".... no one here who wants a terrorist buying a gun or getting on a plane."
This gets right to the core of the problem. How do we know who's a terrorist, and who isn't? And if we know someone is a terrorist, why are we dicking around with petty travel restrictions? We should just kill them.
The problem is that the no-fly list isn't a list of people who are terrorists. It's a list of people that our government thinks might be terrorists.
We do that for search warrants already. Why can we not do it for no-fly lists? We have reasonable suspicion that there will be evidence of a crime in a person's residence, we prove it to a judge we get that warrant. I'm not trying to argue, you seem to know, I'm just asking because I don't understand.
A request by government to infringe on someone's right to privacy may be granted by a judge if they determine that there is sufficient reason to
warrant such an exception. But it's a temporary exception and a necessary one to allow police investigators to do their jobs. Once the investigation is complete, the suspects aren't deprived of their rights in perpetuity unless they are found guilty by
due process - they get their day in court.
The no-fly list isn't an investigation. It's a judgement that strips its victims of the right to air travel without
due process. This is exactly the kind of thing the Constitution's due process provisions were designed to prevent. We should not tolerate a government that maintains secret lists of 'enemies' who are deprived of their rights on mere suspicion.