IIRC, it was initially argued by the Bush administration that because the facility was in Cuba, it was exempt from American laws against indefinite detainment, requiring council and forbidding torture and cruel and unusual punishment (sorry... enhanced interrogation), etc. That argument was quickly shot down, though, because obviously an American military base in Cuba is still American property and subject to American laws.

After 9/11 there was this perception (somewhat engineered by the neo-cons, but also organic in that Americans had never experienced anything like that and had a bit of an existential crisis) that American civil liberties and laws had actually made the country weak and had created a loophole that terrorists had been able to exploit. This led to the "new normal", where it was seen as necessary (even a matter of civic duty) to accept ceding our civil rights and liberties in order to allow the government to aggressively pursue the terrorist threat by any means necessary.

This lead to Guantanamo Bay and the normalization of indefinite detainment and torture in American culture, to the increased militarization of American police, to the modern global surveillance panopticon as revealed by Snowden, and the War on Terror.